1. Exercise:
Add these two single precision IEEE 754 numbers: … …0 Left number: 1.101x24 Right number: 1.011x 22= x24 Add mantissa: = x24 The sum is: …0

2. Carry Propagation 2’s complement best 1’s complement twice as long
15 September 2018
Carry Propagation
2’s complement best
1’s complement twice as long
Significant delay reduction using Carry Look Ahead concept

3. Review Binary Addition
15 September 2018
Review Binary Addition

4. Consider Binary Addition
15 September 2018
Consider Binary Addition
Assume 5 bits
2’s complement arithmetic
Carry out

5. Consider Binary Addition
15 September 2018
Consider Binary Addition
Assume 5 bits 1’s complement arithmetic
= 12 + (-7) = 5
Carry
out

6. Consider Binary Addition
15 September 2018
Consider Binary Addition
Assume 5 bits 1’s complement arithmetic
= 12 + (-13) = -1
Carry
out

7. Consider Binary Addition
15 September 2018
Consider Binary Addition
Assume 5 bits 1’s complement arithmetic
10 – 3 = 10 + (-3) = 7
Carry
out

8. Consider Binary Addition
15 September 2018
Consider Binary Addition
Assume 5 bits
1’s complement arithmetic
Carry
out

9. 4 Bit 1’s Complement Adder
15 September 2018
4 Bit 1’s Complement Adder
Note: carry ripple doubles
Using 1’s complement representation in arithmetic operations
is slow!

10. Quiz 3
Assume we use 4-bit 2’s complement representation to add two integers, give examples where the sum of two numbers results an overflow:
Adding two positives
Adding two negatives
Subtracting a positive from a negative