Number Systems

Jubayer Alam Shoikat

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  • 1. Number Systems
  • 2. Learning Objectives In this chapter you will learn about: • Non-positional number system • Positional number system • Decimal number system • Binary number system • Octal number system • Hexadecimal number system (Continued on next slide)
  • 3. Learning Objectives (Continued from previous slide..) Convert a number’s base • Another base to decimal base • Decimal base to another base • Some base to another base Shortcut methods for converting • Binary to octal number • Octal to binary number • Binary to hexadecimal number • Hexadecimal to binary number Fractional numbers in binary number • • system•
  • 4. Number Systems Two types of number systems are: Non-positional number systems• Positional number systems•
  • 5. Non-positional Number Systems Characteristics • Use symbols such as I for 1, II for 2, III for 3, IIII for 4, IIIII for 5, etc • Each symbol represents the same value regardless of its position in the number • The symbols are simply added to find out the value of a particular number • Difficulty• It is difficult to perform number system arithmetic with such a•
  • 6. Positional Number Systems Characteristics• Use only a few symbols called digits• These symbols represent different values depending• on the position they occupy in the number (Continued on next slide)
  • 7. Positional Number Systems (Continued from previous slide..) The value of each digit is determined by:• 1. 2. 3. The digit itself The position of the digit in the number The base of the number system (base = system) total number of digits in the number The maximum value of a single digit is always equal to one less than the value of the base •
  • 8. Decimal Number System Characteristics A positional number system Has 10 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, • • 8, 9). Hence, its base = 10 The maximum value of a single digit is 9 (one less than the value of the base) • Each position of a digit represents a specific• power of the We use this life base (10) number system in our day-to-day• (Continued on next slide)
  • 9. Decimal Number System (Continued from previous slide..) Example 258610 = (2 x 103) + (5 x 102) 101) x 100)+ (8 x + (6 = 2000 + 500 + 80 + 6
  • 10. Binary Number System Characteristics A positional number system Has only 2 symbols or digits (0 and 1). Hence its base = 2 The maximum value of a single digit is 1 (one less than the value of the base) Each position of a digit represents a specific power of the base (2) • • • • This number system is used in computers• (Continued on next slide)
  • 11. Binary Number System (Continued from previous slide..) Example 101012 = (1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) x (1 x 20) = 16 + 0 + 4 + 0 + 1 = 2110
  • 12. Representing Numbers in Different Number Systems In order to be specific about which number system we theare referring to, it is a common practice to indicate base as a subscript. Thus, we write: 101012 = 2110
  • 13. Bit • Bit stands for binary digit • A bit in computer terminology means either a 0 or a 1 • A binary number number consisting of n bits is called an n-bit
  • 14. Octal Number System Characteristics A positional number system Has total 8 symbols or digits Hence, its base = 8 • • (0, 1, 2, 3, 4, 5, 6, 7). The maximum value of a single digit is 7 (one less than the value of the base • Each position of a digit represents a specific power of• the base (8) (Continued on next slide)
  • 15. Octal Number System (Continued from previous slide..) • Since there are only 8 digits, 3 bits (23 = 8) are sufficient to represent any octal number in binary Example 20578 = = (2 x 83) + (0 x 82) + (5 x 81) + (7 x 80) 1024 + 0 + 40 + 7 = 107110
  • 16. Hexadecimal Number System Characteristics A positional number system Has total 16 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, • • 8, 9, A, B, C, D, E, F). Hence its base = 16 The symbols A, B, C, D, E and F represent the decimal values 10, 11, 12, 13, 14 and 15 respectively • The maximum than the value value of a single of the base) digit is 15 (one less• (Continued on next slide)
  • 17. Hexadecimal Number System (Continued from previous slide..) • Each position of a digit represents a specific power of the base (16) • Since there are only 16 digits, 4 bits (24 = 16) are sufficient to represent any hexadecimal number binary in Example 1AF16 = = = = (1 x 162) + (A x 161) + (F x 160) 1 x 256 + 10 x 16 + 15 x 1 256 + 160 + 15 43110
  • 18. Converting a Number of Another Base to a Decimal Number Method Step 1: Determine the column (positional) value of each digit Step 2: Multiply the obtained column values by the digits in the corresponding columns Step 3: Calculate the sum of these products (Continued on next slide)
  • 19. Converting a Number Decimal Number (Continued from previous slide..) of Another Base to a Example 47068 = ?10 Common values multiplied by the corresponding digits 47068 = 4 x 83 + 7 x 82 + 0 x 81 + 6 x 80 = = = 4 x 512 + 7 2048 + 448 250210 x 64 + 0 + 6 x 1 + 0 + 6 Sum of these products
  • 20. Converting a Decimal Number to a Number of Another Base Division-Remainder Method Step 1: Divide the decimal number to be converted by the value of the new base Step 2: Record the remainder from Step 1 as the therightmost new base digit (least significant digit) of number Step 3: Divide the quotient of the previous divide by the new base (Continued on next slide)
  • 21. Converting a Decimal Number to a Number of Another Base (Continued from previous slide..) Step 4: Record the remainder from Step 3 as the next digit (to the left) of the new base number Repeat Steps 3 and 4, recording remainders from right to left, until the quotient becomes zero in Step 3 Note that the last remainder thus new obtained will be the most significant digit (MSD) of the base number (Continued on next slide)
  • 22. Converting a Decimal Another Base (Continued from previous slide..) Number to a Number of Example 95210 = ?8 Solution: 9528 Remainder s 0 7 6 1 Hence, 95210 = 16708 119 14 1 0
  • 23. Converting a Number of Some Base to a Number of Another Base Method Step 1: Convert the original number to a decimal number (base 10) Step 2: Convert the decimal number so obtained to the new base number (Continued on next slide)
  • 24. Converting a Number of Another Base (Continued from previous slide..) of Some Base to a Number Example 5456 = ?4 Solution: Step 1: Convert from base 6 to base 10 5456 = 5 x 62 + 4 x 61 + 5 x 60 = 5 x 36 + 4 x 6 + 5 x 1 = 180 + 24 + 5 = 20910 (Continued on next slide)
  • 25. Converting a Number of Some of Another Base (Continued from previous slide..) Base to a Number Step 2: Convert 20910 to base 4 4 Remainders 1 0 1 3 Hence, 20910 = 31014 So, 5456 = 20910 = 31014 Thus, 5456 = 31014 209 52 13 3 0
  • 26. Shortcut Method for Converting a Binary Number to its Equivalent Octal Number Method Step 1: Divide the digits into groups of three starting from the right Step 2: Convert each group of three binary digits to toone octal digit using the method of binary decimal conversion (Continued on next slide)
  • 27. Shortcut Method for Converting a Binary to its Equivalent Octal Number (Continued from previous slide..) Number Example 11010102 = ?8 Step 1: Divide the binary digits into from right groups of 3 starting 001 101 010 Step 2: Convert each group into one octal digit 0012 1012 0102 = = = 0 1 0 x x x 22 22 22 + + + 0 0 1 x x x 21 21 21 + + + 1 1 0 x x x 20 20 20 = = = 1 5 2 Hence, 11010102 = 1528
  • 28. Shortcut Method for Converting an Octal Number to Its Equivalent Binary Number Method Step 1: Convert number decimal each octal digit to a 3 digit binary (the octal digits may be treated as for this conversion) Step 2: Combine all the resulting binary single groups binary(of 3 digits each) into a number (Continued on next slide)
  • 29. Shortcut Method for Converting an Octal Number to Its Equivalent Binary Number (Continued from previous slide..) Example 5628 Step = ?2 1: Convert each octal digit to 3 binary digits 58 = 1012, 68 = 1102, 28 = 0102 Step 2: Combine the binary groups 5628 = 101 5 110 6 010 2 Hence, 5628 = 1011100102
  • 30. Shortcut Method for Converting a Binary Number to its Equivalent Hexadecimal Number Method Step 1: Divide the binary digits into groups of four starting from the right Step 2: Combine each group of four binary digits to one hexadecimal digit (Continued on next slide)
  • 31. Shortcut Method for Converting a Binary Number to its Equivalent Hexadecimal Number (Continued from previous slide..) Example 1111012 = ?16 Step 1: Divide the binary digits into groups of four starting from the right 0011 1101 Step 2: Convert each group into a hexadecimal digit 00112 = 0 x 11012 = 1 x 23 23 + 0 x + 1 x 22 22 + 1 x + 0 x 21 21 + + 1 1 x x 20 20 = = 310 1310 = = 316 D16 Hence, 1111012 = 3D16
  • 32. Shortcut Method for Converting a Hexadecimal Number to its Equivalent Binary Number Method Step 1: Convert the decimal equivalent of each hexadecimal digit to a 4 digit binary number Step 2: Combine all the resulting binary groups (of 4 digits each) in a single binary number (Continued on next slide)
  • 33. Shortcut Method for Converting a Hexadecimal Number to its Equivalent Binary Number (Continued from previous slide..) Example 2AB16 = ?2 Convert each hexadecimal binary number Step 1: digit to a 4 digit 216 A16 B16 = = = 210 1010 1110 = = = 00102 10102 10112
  • 34. Shortcut Method for Converting a Hexadecimal Number to (Continued from previous slide..) its Equivalent Binary Number Step 2: Combine the binary 1010 A groups 1011 B 2AB16 = 0010 2 Hence, 2AB16 = 0010101010112
  • 35. Key Words/Phrases Base Binary Binary Bit • • • • • • • • Least Significant Digit (LSD) Memory dump Most Significant Digit (MSD) Non-positional number system Number system Octal number system • • • • number point system Decimal number system Division-Remainder Fractional numbers technique • • •Hexadecimal number system Positional number system

The Real Number System

A Math 10C Collection of Graphical Interpretations

The math equivalent of interpretive dancing?

Brooke and Molly

Whole numbers

Rational numbers

Irrational numbers

Imaginary numbers

5 i 2 = -25

Real numbers

Natural numbers

Real Numbers ex: 2, sqrt(3), 7/22, -45/46, -9

Rational Numbers ex: 6/7, -4.56, -5/7, 4500009234

Integers ex: -4, 98989, 67, -6, -9000

Whole Numbers

Ex: 0, 2, 5, 88

Natural Numbers

Ex: 1, 2, 6, 8, 99

ex: sqrt(2), π

Ex: sqrt(-2),

J U L I A S ’ S L I D E

Jacob ’ s Slide

Fynn and Emma

Real Number System

Real numbers can be represented on a number line (includes irrational and rational numbers.)

Rational numbers can be written as a ratio/fraction.

Irrational numbers cannot be expressed as a ratio/fraction because their decimal form does not end nor is it a repetitive pattern.

Natural numbers are positive integers otherwise known as non-negative numbers that are not a fraction.

Whole numbers are “counting” numbers including 0.

Integers include all “Whole numbers” as well as their negative counterparts.

Imaginary numbers are numbers made by combining an imaginary unit (i) with a real number. They are a negative real number’s square root.

Elizabeth & Erin

~narcissism~

I dabble Sage/Clayton

♡ Isie and Lily’s slide♡ (✿●︿●)

Claire and Liza

Natural: Whole numbers that are positive. Not including zero.

Whole: Positive whole numbers. Including zero.

Integers: All whole numbers, including negatives and zero.

Rational: number with an end, and/or whose next number is predictable.

Irrational: A number with no definitive end, and whose next number cannot be predicted.

Real: A number with a value that can be put on a number line.

Imaginary: The square root of a negative number.

Victoria and Sarah

Real Number: Any number that has a value and can be put on the number line.

Irrational Number: A number that does that does not have a definitive end and the next digit is not predictive.

Rational Number: A number that has a definitive end or the next digit is predictive.

Integer Number: A number excluding fractions and decimals and can be negative, positive, and zero.

Whole: A number excluding decimals and fractions, positive, including zero.

Natural: Positive whole numbers not including zero.

Real Numbers

Irrational Number

Imaginary Numbers

Imaginary Numbers: A number that has a negative square root represented by i

Imaginary Irrational Numbers: A number that does that does not have a definitive end and the next digit is not predictive and has a negative square root

Imaginary Rational: A number that has a definitive end or the next digit is predictive and has a negative square root

Imaginary Integers: A number excluding fractions and decimals and can be negative, positive, and zero and has a negative square root

Imaginary Whole Numbers: A number excluding decimals and fractions, positive, including zero and has a negative square root

Imaginary Natural: Positive whole numbers not including zero.

i Irrational

Imaginary #s

Rational #s

Positive Whole #s above and including 1

All positive #s with no decimals

All whole rational #s without decimals

All #s that have repeating or ending decimals

Square root of a negative and 0

By: Sebastien and Matthew

All numbers except Imaginary numbers

Irrational #s

A # with an infinite # of decimals that never repeat

√ of a negative and 0

Irrational Numbers

Numbers with an infinite number of decimals that never repeat

By Julian & Sasha

Kyra and Danica Real Number System

Numbers which cannot be represented as a fraction. Numbers with an infinite decimal are irrational.

1, 2, 3, 4, 5, 6

0, 1, 2, 3, 4, 5

Any negative or positive number without a decimal

…-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...

Any number which can be represented as a fraction. Decimals which have an end, or have a repeating group are rational.

4.2, 73.823954,

An imaginary number is any i, 3 i, -7i, 21.4372 i, π i, 0 (both real and imaginary).

Real number multiplied by

the imaginary unit i, where i² = -1

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7th Grade Math Number System

Apr 03, 2019

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7th Grade Math Number System. Number System Unit Topics. Click on the topic to go to that section. Number System, Opposites & Absolute Value. Comparing and Ordering Rational Numbers. Adding Rational Numbers. Turning Subtraction Into Addition.

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7th Grade Math Number System Unit 1: The Number System

Number System Unit Topics Click on the topic to go to that section • Number System, Opposites & Absolute Value • Comparing and Ordering Rational Numbers • Adding Rational Numbers • Turning Subtraction Into Addition • Adding and Subtracting Rational Numbers Review • Multiplying Rational Numbers • Dividing Rational Numbers • Operations with Rational Numbers • Converting Rational Numbers to Decimals Common Core Standards: 7.NS.1, 7.NS.2, 7.NS.3 Unit 1: The Number System

Number System, Opposites & Absolute Value Return to Table of Contents Unit 1: The Number System

1 Do you know what an integer is? Yes No Unit 1: The Number System

Number System Rational Real 1/3 Integer 5/2 Whole 0.22 Natural 1,2,3... Irrational 1/5 -3/4 0 ...-4, -3, -2, -1 8.3 -1/11 -2.756 Unit 1: The Number System

Define Integer Definition of Integer: The set of whole numbers, their opposites and zero. X Examples of Integer: {...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...} Unit 1: The Number System

Define Rational Definition of Rational: A number that can be written as a simple fraction (Set of integers and decimals that repeat or terminate) X Examples of rational numbers: , ½ 9 0, -5, 8, 0.44, -0.23, Unit 1: The Number System

Define Irrational Definition of Irrational: A real number that cannot be written as a simple fraction X Examples of irrational numbers: Unit 1: The Number System

Classify each number as specific as possible: Integer, Rational or Irrational 5 ¾ 3.2 -6 -21 1 ½ π 9 3¾ 5 0 -6.32 -65 2.34437 x 103 integer rational irrational Unit 1: The Number System

Rational Numbers on a Number Line Negative Numbers Positive Numbers Zero -5 -4 -3 -2 -1 1 2 0 3 4 5 Numbers to the right of zero are greater than zero Numbers to the left of zero are less than zero Zero is neither positive or negative Unit 1: The Number System

2 Which of the following are examples of integers? -5 A B 0 -3.2 C D 12 1 2 E Unit 1: The Number System

3 Which of the following are examples of rational numbers? 1 3 A B -3 10 C D 0.25 E 75% Unit 1: The Number System

Numbers In Our World Unit 1: The Number System

Numbers can represent everyday situations You might hear "And the quarterback is sacked for a loss of 5 yards." This can be represented as an integer: -5 Or, "The total snow fall this year has been 6 inches more than normal." This can be represented as an integer: +6 or 6 Unit 1: The Number System

Write a number to represent each situation: Spending $6.75 Gain of 11 pounds Depositing $700 10 degrees below zero 8 strokes under par (par = 0) feet above sea level Unit 1: The Number System

4 Which of the following numbers best represents the following scenario: The effect on your wallet when you spend $10.25. A -10.25 B 10.25 C 0 D +/- 10.25 Unit 1: The Number System

5 Which of the following integers best represents the following scenario: Earning $50 shoveling snow. A -50 B 50 C 0 D +/- 50 Unit 1: The Number System

Which of the following numbers best represents the following scenario: You dive feet to explore a sunken ship. 6 A B C 0 D Unit 1: The Number System

Opposites The numbers -4 and 4 are shown on the number line. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 9 8 10 Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero. The numbers -4 and 4 are opposites. Opposites are two numbers which are the same distance from zero. Unit 1: The Number System

7 What is the opposite of -7? Unit 1: The Number System

8 What is the opposite of 18.2? Unit 1: The Number System

What happens when you add two opposites? Try it and see... Click to Reveal A number and its opposite have a sum of zero. Numbers and their opposites are called additive inverses. Unit 1: The Number System

Jeopardy • Integers are used in game shows. • In the game of Jeopardy you: • gain points for a correct response • lose points for an incorrect response • can have a positive or negative score Unit 1: The Number System

When a contestant gets a $100 question correct: Score = $100 Then a $50 question incorrect: Score = $50 Then a $200 question incorrect: Score = -$150 How did the score become negative? Let's take a look... Unit 1: The Number System

Let's organize our thoughts... Question Answered Integer Representation New Score When a contestant gets a $100 question correct Then a $50 question incorrect Then a $200 question incorrect 100 Correct 100 100 50 Incorrect 50 -50 200 Incorrect -200 -150 Unit 1: The Number System

Now you try... Question Answered Integer Representation New Score When a contestant gets a $150 question incorrect Then a $50 question incorrect Then a $200 question correct 150 Incorrect -150 -150 50 Incorrect -200 -50 200 Correct 200 0 Unit 1: The Number System

Now you try... Question Answered Integer Representation New Score When a contestant gets a $50 question incorrect Then a $150 question correct Then a $200 question incorrect Unit 1: The Number System

9 After the following 3 responses what would the contestants score be? $100 incorrect $200 correct $50 incorrect Unit 1: The Number System

10 After the following 3 responses what would the contestants score be? $200 correct $50 correct $300 incorrect Unit 1: The Number System

11 After the following 3 responses what would the contestants score be? $150 incorrect $50 correct $100 correct Unit 1: The Number System

12 After the following 3 responses what would the contestants score be? $50 incorrect $50 incorrect $100 incorrect Unit 1: The Number System

13 After the following 3 responses what would the contestants score be? $200 correct $50 correct $100 incorrect Unit 1: The Number System

To Review • An integer is a whole number, zero or its opposite. • A rational number is a number that can be written as a simple fraction. • An irrational number is a number that cannot be written as a simple fraction. • Number lines have negative numbers to the left of zero and then positive numbers to the right. • Zero is neither positive nor negative. • Numbers can represent real life situations. X Unit 1: The Number System

Absolute Value of Numbers The absolute value is the distance a number is from zero on the number line, regardless of direction. Distance and absolute value are always non-negative (positive or zero). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 What is the distance from 0 to 5? 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7 -2 What is the distance from 0 to -5? Unit 1: The Number System

Absolute value is symbolized by two vertical bars |4| This is read, "the absolute value of 4" 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 What is the | 4 |? Unit 1: The Number System

Use the number line to find absolute value. Move to check |9.6| = 9.6 Move to check |-9| = 9 4 Move to check |-4| = 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Unit 1: The Number System

14 Find Unit 1: The Number System

15 Find |-8| Unit 1: The Number System

16 What is ? Unit 1: The Number System

17 What is ? Unit 1: The Number System

18 Find Unit 1: The Number System

19 What is the absolute value of the number shown in the generator? (Click for web site) Unit 1: The Number System

20 Which numbers have 15 as their absolute value? -30 A B -15 0 C D 15 30 E Unit 1: The Number System

21 Which numbers have 100 as their absolute value? -100 A B -50 0 C D 50 100 E Unit 1: The Number System

Comparing and Ordering Rational Numbers Return to Table of Contents Unit 1: The Number System

Use the Number Line To compare rational numbers, plot points on the number line. The numbers farther to the right are larger. The numbers farther to the left are smaller. 7 4 8 -1 -10 -7 -5 -4 -2 10 -9 -8 -6 -3 9 6 0 3 5 2 1 Unit 1: The Number System

Place the number tiles in the correct places on the number line. Unit 1: The Number System

Now, can you see: Which integer is largest? Which is smallest? Unit 1: The Number System

Where do rational numbers go on the number line? Go to the board and write in the following numbers: Unit 1: The Number System

Put these numbers on the number line. Which number is the largest? The smallest? Unit 1: The Number System

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Number Systems Introduction

Number Systems Introduction

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

the_pink_furby

Last updated

13 March 2024

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make a presentation on number system

This package includes two worksheets and a editable Powerpoint presentation that gives the teacher definitions for different number systems, as well as two seperate tasks testing a student knowledge and understanding. Great as an introduction to number systems for both Mathmatics and Computer science. The powerpoint can be edited.

2 PDF files of questions 2 PDF files of questions and answers Microsoft PowerPoint Product information guide Questions on the following topics Real Irrational Rational Integers Ordinal Binary Features include

Answer grid Questions PowerPoint of definitions set out as both a teaching tool Definitions set out to be used as Posters Use of graphics Editable sections - PowerPoint only

All text (font, colours, sizes) Addition slides Any issues please contact [email protected] any time and I am happy to help or add future features.

Total Pages Answer Key Included Teaching Duration 45 minutes

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Opinion | Stephanie Kollmann: Illinois legislators should…

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Opinion | Stephanie Kollmann: Illinois legislators should create a statewide system for public defense

Senate President Don Harmon departs after Gov. J.B. Pritzker delivered his State of the State and budget address before the General Assembly at the Illinois Capitol on Feb. 21, 2024. (Brian Cassella/Chicago Tribune)

If you or your loved one were accused of a crime, you would be desperate for an attorney to gather and present any of this information to the court. The right to a strong defense, guaranteed in the Sixth Amendment to the Constitution, is a bedrock American principle. But, despite the heroic efforts of public defense attorneys across the state, it remains little more than an ideal for many Illinoisans accused of a crime who cannot come up with the money needed to mount a robust defense. 

A 2021 report on Illinois public defense funded by the U.S. Department of Justice and commissioned by the Illinois Supreme Court is clear: Current conditions have resulted in people being denied their rights. Multiple studies — including a multiyear, interdisciplinary assessment of public defense budgets and projected staffing levels in each of Illinois’ 102 counties led by my colleague Julie Biehl at the Northwestern University Pritzker School of Law — have documented:

  • Public defense is inadequately staffed and resourced in each of Illinois’ 102 counties. Public defenders across the state have lacked money to pay for paralegals, case management systems, office space, social workers, mental health experts and investigators — even for databases to research the law.
  • On top of baseline deficiencies, broad geographic disparities in county funding and wide racial disparities in caseloads result in the rights of rural, Black and Latino clients being most affected by the lack of resources.  
  • While every county has a full-time state’s attorney, in 60% of Illinois counties, there is no full-time county public defender. Instead, in those counties, judges appoint local private practice attorneys using flat-fee contracts, which the American Bar Association says are unacceptable because they “reward counsel for doing as little work as possible.” In rural areas, one attorney may be responsible for the defense work in multiple counties at once. It is a testament to their passion that so many publicly paid defense attorneys continue to work their fingers to the bone under such circumstances — but it should not be necessary, and most importantly, it still leaves clients suffering from resource gaps.
  • Judges outside of Cook County appoint and remove chief public defenders at will — and attorneys who have spoken out about unconstitutional conditions and impossible workloads in their office have been summarily removed on more than one occasion. Public defense budgets are set and managed by local elected officials, judges or both, despite national standards that call for a system that is independent and insulated from judicial conflicts of interest and political winds.
  • Although the state of Illinois is responsible for ensuring that public defense is adequately and effectively provided, it currently has no way to track whether this is happening or what the consequences are. What are  the current workloads? Do they violate national standards? How quickly are additional resources delivered when they are needed? The state of Illinois could be sued over the answers to these questions — but currently cannot answer them, much less manage them.

The good news is that there is a solution. And there is support in Springfield to make it happen.

Under the leadership of Senate President Don Harmon and the Illinois Supreme Court, the Illinois General Assembly put this issue on the legislative agenda in April, urging consideration of a statewide office to provide public defenders with support they so badly need.

“With our increased emphasis on a fair criminal justice system, it’s critical that defendants who can’t afford counsel have access to a public defender,” Harmon said in the Tribune last month. He said his goal was to promote further negotiations with criminal justice reform advocates and to pass legislation by the end of the session on May 24.

In the true spirit of democracy, those negotiations are happening, and there is now a more detailed proposal pending, one that has extensive feedback from the public defense community, various justice system advocates, and state and national researchers. Known as the Funded Advocacy & Independent Representation, or FAIR, Act, it would immediately address structural deficiencies affecting defense, while allowing for a community- and client-centered, defender-led planning process to build up defense services in every corner of the state.

Legislators should follow the lead of Harmon and create a statewide public defense system that is organized around the needs of clients and responsive to the expertise of public defenders, and builds capacity for the state to meet constitutional standards.

According to the National Registry of Exonerations, Illinois leads the U.S. in wrongful convictions. But these cases, terrible as they are, are the tip of the iceberg, illustrating a much more sizable threat lurking below the surface. Illinois has, for too long, failed to safeguard the rights of people accused of a crime, regardless of their access to money. The new pretrial system that launched with the SAFE-T Act was a critical step toward addressing this problem.

A fully funded public defense system accountable to the public — not to local politicians and judges — is the next needed reform for this session.

Stephanie Kollmann is the policy director for the Children and Family Justice Center at Bluhm Legal Clinic at Northwestern University’s Pritzker School of Law. 

Submit a letter, of no more than 400 words, to the editor here or email [email protected] .

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IMAGES

  1. Number System Presentation

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  2. Number System

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  3. What is Number System and Binary Number System. IGNOU

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  4. PPT ON NUMBER SYSTEM

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VIDEO

  1. Number Systems

  2. PRESENTATION NUMBER 1

  3. 6. Introduction to Number System

  4. English presentation number 2

  5. Number Systems

  6. Number Systems 1 Overview

COMMENTS

  1. Number Systems

    Number Systems Two types. Non-positional Number Systems Characteristics •. Positional Number Systems Characteristics• Use. Positional Number Systems (Continued. Decimal Number System Characteristics A. Decimal Number System (Continued. Binary Number System Characteristics A. Binary Number System (Continued.

  2. Chapter 1: The Real Number System

    1.1: The Real Number System. Sets. A set is a collection of objects or numbers, each of which are called elements or members of the set. The elements of a set are written within braces, so that. A = {4, 5, 6} Tells us that set A consists of the numbers 4, 5, and 6. We can also write 4 ∊A, which is read as "4 belongs to A," or "4 is a ...

  3. PPT

    Introduction to Number Systems. An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Download presentation by click this link.

  4. Number Systems and Operations

    Free Google Slides theme and PowerPoint template. Are you a math teacher struggling to keep your 6th-grade students engaged in learning about number systems and operations? Then, please pay attention, because we have the perfect solution for you! This creative template is designed with interesting illustrations that will capture your students ...

  5. The Real Number System

    Real: A number with a value that can be put on a number line. Imaginary: The square root of a negative number. Victoria and Sarah. Real Number: Any number that has a value and can be put on the number line. Irrational Number: A number that does that does not have a definitive end and the next digit is not predictive.

  6. Introduction to number systems and binary

    The base 10 (decimal) system is the most common number system used by humans, but there are other important and useful number systems. For example, base 2, called binary system, is the basis of modern computing. We can convert between the decimal form and binary form of a number to solve different problems.

  7. Discovering the Origin of the Numbering System Presentation

    This comprehensive package will guide your students, exploring the origin of numbers as such and the different numbering systems resulting from the need to count. With a blend of well-structured content and engaging visuals, this educative template makes learning about the history of numbers a joyful experience. Download this slide deck today ...

  8. Number System Presentation

    Hexadecimal Number System; The hexadecimal number system, also known as base-16, uses sixteen digits (0-9 and A-F) to represent numbers. Each digit's value is determined by its position in the number. Hexadecimal numbers are commonly used in computer programming, particularly for representing memory addresses and color codes.

  9. Number Systems

    The Binary Number System The binary number system is also a positional numbering system. Instead of using ten digits, 0 - 9, the binary system uses only two digits, 0 and 1. Example of a binary number and the values of the positions: 1001 101 26 25 24 23 22 21 20. Converting from Binary to Decimal 101 26 25 24 23 22 21 20 20 1 21 = 2 25 = 32 22 ...

  10. PPT Architecture and Number Systems

    The Hexadecimal Number System (con't) Binary Decimal Hexadecimal Binary Decimal Hexadecimal 0 0 0 1010 10 A 1 1 1 1011 11 B 10 2 2 1100 12 C 11 3 3 1101 13 D 100 4 4 1110 14 E 101 5 5 1111 15 F 110 6 6 111 7 7 1000 8 8 1001 9 9 The Hexadecimal Number System (con't) Example of a hexadecimal number and the values of the positions: 3 C 8 B 0 5 ...

  11. PDF Number Systems and Number Representation

    • The binary, hexadecimal, and octal number systems • Finite representation of unsigned integers • Finite representation of signed integers • Finite representation of rational (floatingpoint) numbers-Why? • A power programmer must know number systems and data representation to fully understand C's . primitive data types. Primitive ...

  12. 7 Best Number System-Themed Templates for PowerPoint & Google Slides

    7 Best Number System-Themed Templates. CrystalGraphics creates templates designed to make even average presentations look incredible. Below you'll see thumbnail sized previews of the title slides of a few of our 7 best number system templates for PowerPoint and Google Slides. The text you'll see in in those slides is just example text.

  13. PPT

    Decimal Number system • Decimal number system contains 10 digits: 0,1,2,3,4,5,6,7,8,9; and that is why its base or radix is 10. • Here radix means total number of digits used in any system. Decimal Number System • The decimal number system is a positional number system. • Example: • 5 6 2 1 1 X 100 = 1 • 103 102 101 100 2 X 101 = 20 ...

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    Download Free and Premium Number System PowerPoint Templates. Choose and download Number System PowerPoint templates, and Number System PowerPoint Backgrounds in just a few minutes.And with amazing ease of use, you can transform your "sleep-inducing" PowerPoint presentation into an aggressive, energetic, jaw-dropping presentation in nearly no time at all.

  15. PDF Number Systems and Number Representation

    The Binary Number System Name • "binarius" (Latin) => two Characteristics • Two symbols • 0 1 • Positional • 1010 B ≠ 1100 B Most (digital) computers use the binary number system Terminology • Bit: a binary digit • Byte: (typically) 8 bits 6 Why?

  16. Free Numbers PowerPoint Templates & Google Slides Themes

    Free Number Slide Templates for an Engaging Slideshow. Make your data-driven presentations shine with a numbers PowerPoint template. Whether you're a business analyst, researcher, or student, these templates will help you convey your numerical information with clarity and impact. With a range of customizable slides, you can easily organize and ...

  17. PPT

    Presentation Transcript. 7th Grade Math Number System Unit 1: The Number System. Number System Unit Topics Click on the topic to go to that section • Number System, Opposites & Absolute Value • Comparing and Ordering Rational Numbers • Adding Rational Numbers • Turning Subtraction Into Addition • Adding and Subtracting Rational ...

  18. Number Systems Introduction

    zip, 198.52 KB. This package includes two worksheets and a editable Powerpoint presentation that gives the teacher definitions for different number systems, as well as two seperate tasks testing a student knowledge and understanding. Great as an introduction to number systems for both Mathmatics and Computer science. The powerpoint can be edited.

  19. ppt on number system

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  20. 15 Best Presentation Software for 2024 (Full Comparison Guide)

    Google Slides is the presentation software available via your Google account. Just like you can create documents and spreadsheets with Google Docs and Sheets, you can create presentations with Google Slides. The setup is very similar to PowerPoint and is free to use for anyone with a google account.

  21. Guilds FAQ

    How to make Changes to your Guild. 1. Navigate to the Guild you want to make changes to. 2. Tap on the server name in the top-left and then tap on Server Settings and then navigate to the Guild Settings tab. 3. Here you can go through any of your Guild settings and make adjustments as needed. Once finished, tap on Save & Exit in the top-right ...

  22. Op-ed: Illinois should create a statewide public defense system

    Legislators should follow the lead of Harmon and create a statewide public defense system that is organized around the needs of clients and responsive to the expertise of public defenders, and ...