Answer to Question #162744 in Electric Circuits for Aarati

Question

Implement the following combinational logic circuits 

a) Half-adder

b) Full-adder

c) Half- Subtractor

d) Full- Subtractor

Answer 1

(a) Half adder:-

Truth table:

The sum of product(SOP) form for Sum and carry of half adder is given by,

$\text{Sum},S=\bar{A}.B+A.\bar{B}\\\text{carry},C=A.B$

The logic circuit of half Adder is-

(b) Full Adder:-

Truth table:-

The sum of product(SOP) form for Sum and carry of full adder is given by,

$\text{Sum},S=\bar{A}.\bar{B}.C+A.\bar{B}.C+A.\bar{B}.\bar{C}+A.B.C\\\text{carry},C=A.B+C_{in}(A.\bar{B}+\bar{A}.B)$

The logic circuit of Full Adder is-

(C) Half Subtractor:-

Truth table:-

The sum of product(SOP) form for Difference and Borrow of half subtractor is given by,

$\text{Difference},D=\bar{A}.B+A.\bar{B}\\\text{Borrow},B_i=\bar{A}.B$

The logic circuit of half Subtractor is-

(iv) Full Subtractor:-

Truth table-

The sum of product(SOP) form for Difference and Borrow of full subtractor is given by,

$\text{Difference},S=\bar{A}.\bar{B}.C+A.\bar{B}.C+A.\bar{B}.\bar{C}+A.B.C\\\text{Borrow},C=\bar{A}.\bar{B}.C+\bar{A}.B.\bar{C}+\bar{A}.B.C+A.B.C$

The logic circuit of Full subtractor is-