Question

Assuming signed two’s complement representation using m=8 bits, add the following numbers using binary addition AND determine the values of the N, Z, V and C flags in response to each calculation.

1. (-128) + (+100)

2. (+5) + (+7)

3. (+5) + (-7)

4. (-5) + (+7)

5. (-5) + (-7)

6. (+120) + (+100)

7. (-120) + (-100)

8. (6A)₁₆+ (E2)₁₆

9. (A7)₁₆+ (35)₁₆

10. (80)₁₆+ (80)₁₆

Answer 1

Now let's find each number in signed 2's complement representation. For positive numbers we just need to find it's signed 1's complement. For negative number we need to add 1 to the signed 1's complement.

i

Now +100 = 0110 0100

-128 = 1000 0000. Hence the result will be 1110 0100.

ii

+5 = 0000 0101

+7 = 0000 0111

Result = 0000 1100

iii Here -7 = 1111 1001 and +5 =  0000 0101 hence result =  1111 1110

iv

-5 = 1111 1011

+7 = 0000 0111

result = 1 0000 0010 ( Overflow will occur)

v

-5 + -7 = 1111 1011 + 1111 1001 = 1 1111 0100 (Overflow will occur)

vi

120 + 100 = 0111 1000 + 0110 0100 = 1101 1100 . Result got negative because range of +127 exceeded.

vii

Now -120 + -100 = 1000 1000 + 1001 1100 = 1 0010 0100 (Overflow)

viii

6A + E2 = 0110 1010 + 1110 0010 = 1 0100 1100 (Overflow)

ix

A7 + 35 = 1110 0010 + 0011 0101 = 1 0001 0111 (Overflow)

x

80+80 = 1000 0000 + 1000 0000 = 1 0000 0000 (Overflow and Zero Result)

Now we will indicate the status of flags (N,Z,V,C) for all of the above . Note the order of bits below correspond to order in (NZVC)

i . (1000)

ii (0000)

iii (1000)

iv (0010)

v (1010)

vi (1000)

vii (0010)

viii (0010)

ix (0010)

x (0110)