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CS33-1

# CS33-1 - CS 33 Computer Organization Topic 1 Number Bases...

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-1 CS 33: Computer Organization Topic 1 Number Bases

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-2 Number Bases Base Name Base Number Digits
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-3 Number Bases Base Name Base Number Digits Decimal 10 0 - 9

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-4 Decimal Numbers Base 10 Digits 0 – 9 Digit positions are powers of 10 10 3 10 2 10 1 10 0 1 2 3 4 1234 = 4 * 10 ^ 0 = 4 + 3 * 10 ^ 1 = 30 + 2 * 10 ^ 2 = 200 + 1 * 10 ^ 3 = 1,000 1,234
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-5 Conversion to Decimal Assume Base b: Digits are 0 to b - 1 Digit positions are powers of b Multiply each digit by power of b and add products Example: d 3 d 2 d 1 d 0 Powers of b: b 3 b 2 b 1 b 0 Base b digits: d 3 d 2 d 1 d 0 d 3 d 2 d 1 d 0 = d 0 * b ^ 0 + d 1 * b ^ 1 + d 2 * b ^ 2 + d 3 * b ^ 3

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-6 Octal Numbers Base 8 Digits 0 – 7 Digit positions are powers of 8 8 3 8 2 8 1 8 0 1 2 3 4 1234 8 = 4 * 8 ^ 0 = 4 10 + 3 * 8 ^ 1 = 24 10 + 2 * 8 ^ 2 = 128 10 + 1 * 8 ^ 3 = 512 10 668 10
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-7 Number Bases Base Name Base Number Digits Decimal 10 0 - 9 Octal 8 0 - 7

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-8 Octal Number Practice Convert 12345 8 to decimal
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-9 Octal Number Practice Convert 12345 8 to decimal Use powers of 8 8 4 8 3 8 2 8 1 8 0 1 2 3 4 5 12345 8 = 5 * 8 ^ 0 = 5 10 + 4 * 8 ^ 1 = 32 10 + 3 * 8 ^ 2 = 192 10 + 2 * 8 ^ 3 = 1,024 10 + 1 * 8 ^ 4 = 4,096 10 5,349 10

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-10 Binary Numbers Base 2 Digits 0 and 1 Digit positions are powers of 2 2 3 2 2 2 1 2 0 1 0 1 1 1011 2 = 1 * 2 ^ 0 = 1 10 + 1 * 2 ^ 1 = 2 10 + 0 * 2 ^ 2 = 0 10 + 1 * 2 ^ 3 = 8 10 11 10
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-11 Number Bases Base Name Base Number Digits Decimal 10 0 - 9 Octal 8 0 - 7 Binary 2 0, 1

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-12 Binary Number Practice Convert 110100101 2 to decimal
CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-13 Binary Number Practice Convert 110100101 2 to decimal Use powers of 2 for nonzero digits 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 1 0 1 0 0 1 0 1 110100101 2 = 1 * 2 ^ 0 = 1 10 + 1 * 2 ^ 2 = 4 10 + 1 * 2 ^ 5 = 32 10 + 1 * 2 ^ 7 = 128 10 + 1 * 2 ^ 8 = 256 10 421 10

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CS 33: Computer Organization Topic 1: Number Bases 9/2008 John A. Rohr All Rights Reserved JAR 1-14 Hexadecimal Numbers Base 16 Digits 0 – 9, A, B, C, D, E, and F Digit positions are powers of 16 16 3 16 2 16 1 16 0 1 2 3 4 1234 16 = 4 * 16 ^ 0 = 4 10 + 3 * 16 ^ 1 = 48 10 + 2 * 16 ^ 2 = 512 10 + 1 * 16 ^ 3 = 4,096 10 4,660 10
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