Question

7. Solve the following using 2’s Complement. You are working with a 6-bit register (including sign). Indicate if there’s an overflow or not. a. (-14)+(-28) b. 12+(-16) c. 10+11

Answer 1

The overflow flag is relevant when we are calculating the sum of two signed numbers but it is not relevant to the unsigned number addition.

a.

The given expression is:

= (-14) + (-28)

The binary equivalent of 14 is = 001110

The binary equivalent of -14 is = 110000

The binary equivalent of 28 is = 011100

The binary equivalent of -28 is = 100010

110000 100010 + 010010

There is an overflow.

b.

The given expression is:

= 12 + (-16)

When the sign of two additional operands is different then overflow never occurs.

The binary equivalent of 12 is = 001100

The binary equivalent of 16 is = 010000

The binary equivalent of -16 is = 110000

001100 110000 十 111100

The MSB(Most Significant Bit) is one, so the result is negative and stored in two's complement form.

The result after two's complement is = 000100

So, the result is = -4

There is no overflow.

c.

The given expression is:

= 10 + 11

The binary equivalent of 10 is = 001010

The binary equivalent of 11 is = 001011

001010 001011 + 010101

There is no overflow.

The final result is positive and the result is = 21.