Question

Referring to Friday’s class presentation on “condition flags” (Z=zero, N=negative, C=carry, V=overflow), assume the operation A-B is performed using two’s complement arithmetic. For each of the following six relationships, write a logic expression in terms of Z, N, C, and/or V that evaluates to 1 if that relationship is true, based on the result of A-B.

A = B

A != B (not equal)

A > B

A ≥ B

A < B

A ≤ B

Answer 1

1. A=B

let A=B=9

A= 1001, B=1001, 2's compliment of B= 0111

A-B= 1 0000

Z=1, N=0, C=1, V=1

2. A!=B

let A=9, B=8.

A=1001, B=1000, 2's compliment of B= 1000

A-B= 1 0001

Z=0, N=0, C=1, V=0.

3. A > B

let A=9, B=8.

A=1001, B=1000, 2's compliment of B= 1000

A-B= 1 0001

Z=0, N=0, C=1, V=0.

4. A>=B

let A=9, B=8.

A=1001, B=1000, 2's compliment of B= 1000

A-B= 1 0001

Z=0, N=0, C=1, V=0.

OR

let A=B=9

A= 1001, B=1001, 2's compliment of B= 0111

A-B= 1 0000

Z=1, N=0, C=1, V=1

5. A<B

let A=8, B=9.

A=01000, B=01001, 2's complient of B=10111.

A-B= 11111

Z=0, N=1, C=0, V=0.

6. A<=B

let A=8, B=9.

A=01000, B=01001, 2's complient of B=10111.

A-B= 11111

Z=0, N=1, C=0, V=0.

OR

let A=B=9

A= 1001, B=1001, 2's compliment of B= 0111

A-B= 1 0000

Z=1, N=0, C=1, V=1.

Hence Expression for Z, N, C, V:

Z+N+C+V=1