Binary Adder-Subtractor Circuits: Combining Addition and Subtraction

Learn about binary adder-subtractor circuits and how they efficiently perform both addition and subtraction operations using the two's complement method. This guide includes a detailed explanation and diagram of a 4-bit adder-subtractor circuit.

Binary Adder-Subtractor Circuits

Building a Binary Adder-Subtractor

A binary adder-subtractor circuit combines addition and subtraction operations into a single circuit. It uses the fact that subtraction can be implemented as addition of the two's complement.

Two's Complement

The two's complement of a binary number is obtained by inverting (flipping) all the bits and then adding 1 to the result. This is useful because adding the two's complement of a number is equivalent to subtracting the original number.

4-Bit Adder-Subtractor Circuit

(A block diagram of a 4-bit adder-subtractor circuit should be included here. The diagram should show two 4-bit inputs (A and B), a mode input (M), four full adders, and four sum outputs (S₀-S₃) and a carry output (C₄). An exclusive-OR gate should be shown for each bit of the B input. The connection of the mode input (M) to the XOR gates should be shown, as well as the connection of a 1 to the carry input (C₀) when M is high. A clear explanation of how the circuit functions as both an adder and subtractor, based on the value of M, should be given.)

Adder-Subtractor Operation

The mode input (M) controls whether the circuit performs addition or subtraction:

  • M = 0 (LOW): The circuit acts as an adder. The B inputs pass through the XOR gates unchanged (B ⊕ 0 = B), and the input carry (C₀) is 0. The operation performed is A + B.
  • M = 1 (HIGH): The circuit acts as a subtractor. The B inputs are complemented (B ⊕ 1 = B'), and the input carry (C₀) is 1. The operation performed is A + (2's complement of B), which is equivalent to A - B.

Conclusion

Adder-subtractor circuits demonstrate the efficiency of using logic gates to combine arithmetic operations. By cleverly using the two's complement representation and XOR gates, a single circuit can perform both addition and subtraction.