A combinational circuit is nothing but circuits that are created using simple gate. So logic is applied to the input and bits are sent directly to the output.
There is not MEMORY element like a flip-flop.
The simplest goal of this circuit is to add two bits and give the result. This circuit has 2 input and 2 output.
Let us see what happens when you add two binary digits (OR)
1 + 0 = 1
0 + 1 = 1
0 + 0 = 0
1 + 1 = 0 and 1 as carry
TRUTH TABLE OF HALF-ADDER
C = x.y
S = x’.y + x.y’
The C carry is AND function.
The S sum is XOR function.
LOGIC DIAGRAM OF HALF-ADDER CIRCUIT
From the Truth Table it is clear that we need two gate to implement the half-adder circuit.
Full adder circuit needed when we want to add 3 bits which means there are 3 inputs to the circuit and 2 output.
The outputs are
Let’s see what happens when we add three binary bits(OR).
It would be easier if we draw a Truth Table for the Full Adder circuit.
|TRUTH TABLE FOR FULL-ADDER CIRCUIT|
LOGIC DIAGRAM FOR FULL-ADDER CIRCUIT
We can find the characteristic equation of Full Adder circuit by using K-MAP. From the Truth table find all the minterms that give an sum = 1.
We get following,
Sum = x’y’z + x’yz’ + xy’z’ + xyz
The carry is 1 whenever two or more of three input variable is 1.
C = xy + xz + yz
You can see that we cannot group any of these 1 in the K-MAP fro full adder. Hence,
Sum = m1 + m2 + m4 + m7
FULL-ADDER LOGIC DIAGRAM
Construct full adder circuit diagram using two methods
- Construct using 2 Half-Adder circuits
- Implement using AND,OR and NOT gates.
|CIRCUIT FOR CARRY|
|CIRCUIT FOR SUM IN FULL-ADDER|
We will not see the circuit for Full Adder using two half-adder.
|FULL ADDER CIRCUIT|