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Negative Numbers. Lecture L2.3 Section 2.4. Ignore carry. Negative Numbers. Subtract by adding. 73 -35 38. 73 +65 138. 10’s complement. Negative Numbers. 10’s complement : Subtract from 100. Take 9’s complement and add 1. 100 -35 65. 99 -35 64 +1 65.

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Presentation Transcript
negative numbers

Negative Numbers

Lecture L2.3

Section 2.4

negative numbers1

Ignore carry

Negative Numbers

Subtract by adding

73

-35

38

73

+65

138

10’s complement

negative numbers2
Negative Numbers

10’s complement:

Subtract from 100

Take 9’s complement and add 1

100

-35

65

99

-35

64

+1

65

negative numbers3
Negative Numbers

2’s complement:

Subtract from

Take 1’s complement and add 1

100000000

01001101

10110011

11111111

-01001101

10110010

+1

10110011

finding 2 s complement

Complement

remaining bits

Copy all bits

to first 1

2’s complement

Finding 2’s Complement

0 1 0 1 1 0 0 0

1

0

1

0

1

0

0

0

negative number take 2 s complement
Negative NumberTake 2’s Complement

7510 = 4B16 = 01001011

-7510 = B516 = 10110101

FF

-4B

B4

+1

B5

negative number take 2 s complement1
Negative NumberTake 2’s Complement

110 = 0116 = 00000001

-110 = FF16 = 11111111

12810 = 8016 = 10000000

-12810 = 8016 = 10000000

signed numbers
Signed Numbers

4-bit: 8H = -8 to 7H = +7

1000 to 0111

8-bit: 80H = -128 to 7F = +127

16-bit: 8000H = -32,768 to

7FFFH = +32,767

32-bit: 80000000H = -2,147,483,648 to

7FFFFFFFH = +2,147,483,647

questions
Questions

What is the two’s complement of

00101100?

What hex number represents the

decimal number -40?