4 bit adder subtractor

Question

Design and Compare 4-bit adder/subtractor circuit using two’s and one’s complement for subtraction. Show your design for deducing the correct result (positive or negative) on subtraction.

Answer 1

The implementation is based on the following equation:

A - B = A + 2'sComp(B)

2'sComp (B) = 1'sComp(B) + 1

Notes of the above equation:

1. 2'sComp stands for 2's complement
2. Also we know that 2'sComp = 1'sComp + 1

So to design a single HW that implements both add and subtract operation, you can use a adder unit (ripple adder) with following consideration

1. Assuming the inputs of adder are Ai and Bi
2. you need to put a Mux2x1 behind the Bi input and pass Bi and Bi' as inputs of this Mux2x1
3. The selector of all Mux2x1 components is a control signal which decides you want to do add or subtract operation (lets call it SUB).
4. Assuming SUB=1 we want to do subtract operation, in MUX make sure Bi'is connected to I1 of Mux2x1 and Bi is connected to I0 of Mux2x1
5. We also connect the SUB to Cin of LSB full adder component in ripple adder