To verify the truth table of half adder and full adder.
Digital trainer kit, IC 7486, IC 7432, IC 7408, Connecting wires.
Adder circuit is a combinational digital circuit that is used for adding two numbers. A typical adder circuit produces a sum bit (denoted by S) and a carry bit (denoted by C) as the output. Adder circuits can be used for a lot of other applications in digital electronics like address decoding, table index calculation etc. Adder circuits are of two types: Half adder ad Full adder
Half adder
A half adder is a combinational circuit that performs the sum of two binary digits (A, B) to givea maximum of two binary outputs namely the sum(S) and the carry(C). Carry is the higher order bitand the sum is the lower order bit of the output. Functional Table of the Half-Adder is given below
Functional Table of Half Adder
A | B | Sum | Carry |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
The Boolean expression for the sum (S) and carry(C) of half adder is,
Sum = AB' + A'B = A⊕B
Carry= A.B
Full adder
A full adder is a combinational circuit that performs the sum of three binary digits (A, B, Cin) to give a maximum of two binary outputs namely the sum(S) and the carry- out (Cout).The full adder becomes necessary when a carry input must be added to the two binary digits to obtain the correct sum. A half adder has no input for carries from previous circuits
Functional Table of Full Adder
A | B | C | Sum | Carry |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
The Boolean expression for the sum (S) and carry-out (Cout) of full adder is,
Sum = A'B'C + A'BC' + AB'C' + ABC
Cout = A'BC + AB'C + ABC' + ABC
Simplification of Logic Equations
Sum = A'B'C + A'BC' + AB'C' + ABC
= A’(B’C+BC’) + A(B’C’+BC)
=A⊕B⊕C
Cout = A'BC + AB'C + ABC' +ABC
= A'BC + ABC+ AB'C +ABC'
= AB(C+C’) + C(A’B+AB’)
=AB + C(A⊕B)
The full adder drawn above can be visualized as a combination of two half adders. It uses two XOR gates, the output of 1st XOR gate (i.e. Sum A+B) is taken as input to 2nd XOR gate and the other is the third input( usually the Cin), the outputs of the AND gates which are nothing but the carry of HA are ORed together. The FA drawn as a combination of two HA is shown below.
Result:The truth table of half adder and full adder is verified.
Q1:What is a combinationalcircuit?
Ans:In a combinational circuit, the output depends upon present input(s) only i.e, not dependant on the previous input(s). The combinational circuit has no memory element. It consists of logic gates only
Q2:What is ahalf-adder?
Ans:A logic circuit, that can add two 1-bit numbers and produce outputs for sum and carry, is called a half-adder.
Q3:What is afull-adder?
Ans:A binary adder, which can add two 1-bit binary numbers along with a carry bit and produces outputs for sum and carry is called a full-adder.
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