Explain Arithmetic circuit.

The figure above shows a 4-bit arithmetic circuit. An Arithmetic circuit is the digital circuit that can perform all the arithmetic operations like addition, subtraction, increment and decrement in a single circuit.

The 4-bit arithmetic circuit includes 4 full adders arranged in such a way that the output carry of lower order full adder is the input carry of higher order full adder and 4 multiplexers of 4*1 nature that accepts 4 inputs. The 4 inputs of the multiplexer are the input from A, input from B, logic 0 and logic 1. The operands A and B are applied in the circuit in accordance to their individual bits like A0, A1, A2 and A3 and similarly B0, B1, B2 and B3. C_in is the initial carry and the output is represented by the bit sequence D₃D₂D₁D₀. C_out is the final output carry.

The output of the binary adder is calculated by:

D= A+ Y + C_in

The working of the 4-bit arithmetic circuit is summarized below:

select			Input	Output D=A+Y+Cin	Microoperation
S1	S0	Cin
0	0	0	B	D=A+B	Add
0	0	1	B	D=A+B+1	Add with carry
0	1	0		D=A+	Subtract with borrow
0	1	1		D=A+ +1	Subtract
1	0	0	0	D=A	Transfer A
1	0	1	0	D=A+1	Increment A
1	1	0	1	D=A-1	Decrement A
1	1	1	1	D=A	Transfer A