Question

Q3. The adder below adds two 16-bit numbers X and Y (i.e. S-X+Y), where X-Xi5Xi4...XiXo and Y-Y15Y14...YiYo. Assume we are using two's complement representation for our signed numbers, in which flipping all the bits of a number Y and adding one to it will give-Y. Modify the circuit below by including a signal P that picks whether the circuit will add them as X+Y, or subtract them as X-Y = X+(-Y) Suppose when P=0 the circuit will add and when P-1 it will subtract. Hint: Q XOR 1 flips Q (that is Q XOR 1 Q) 15 15 Carry Out 15 FA FA FA Carry In S15

Answer 1

For performing the operation, X-Y, the 2's complement of Y is taken and added to X.

The 2's complement of a binary number Q is found by taking the complement of every bit, and adding one to the whole number.

So, $\bar{Q} = Q + 1$

Therefore, $X - Y = X + \bar{Y} + 1$

So for subraction to be performed, all the bits in Y have to be complemented, and an additional 1 has to be added. This can be done by taking the carry in, C₀ = 1.

Since P = 1 implies subtraction, Y_i has to be complemented if P = 1. This can be done using an XOR gate with inputs Y_i and P.

The resultant adder is given below:

15 15 ar ry out trn -tn 15 + FA FA Carry In carry t" 15