Exercise: Add these two single precision IEEE 754 numbers: 1 1000 0011 1010…0 1 1000 0001 0110…0 Left number: 1.101x24 Right number: 1.011x 22= 0.01011x24 Add mantissa: 1.101 + 0.01011 = 1.11111x24 The sum is: 1 1000 0011 111110…0
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
Review Binary Addition 15 September 2018 Review Binary Addition
Consider Binary Addition 15 September 2018 Consider Binary Addition Assume 5 bits 2’s complement arithmetic Carry out
Consider Binary Addition 15 September 2018 Consider Binary Addition Assume 5 bits 1’s complement arithmetic 12 - 7 = 12 + (-7) = 5 Carry out
Consider Binary Addition 15 September 2018 Consider Binary Addition Assume 5 bits 1’s complement arithmetic 12 - 13 = 12 + (-13) = -1 Carry out
Consider Binary Addition 15 September 2018 Consider Binary Addition Assume 5 bits 1’s complement arithmetic 10 – 3 = 10 + (-3) = 7 Carry out
Consider Binary Addition 15 September 2018 Consider Binary Addition Assume 5 bits 1’s complement arithmetic Carry out
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!
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