COMBINATIONAL LOGIC CIRCUITS-ENCODER AND DECODER

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TODAY  I GOING TO SHOW YOU SOME QUICK NOTES FOR YOUR VIVA, PRACTICALS AND EXAMS ON THE TOPIC- ENCODER, DECODER.

INTRODUCTION- 

To perform any specific function that can be expressed by a Boolean expression, a combination of logic gates is called a combinational logic circuit.

CLASSIFICATIONS OF CIRCUITS-

(A) Combinational circuit

(B) Sequential circuit

ENCODERS-

An encoder in digital electronics is a one-hot to binary converter. That is, if there are 2ⁿ input lines, and at most only one of them will ever be high, the binary code of this 'hot' line is produced on the n-bit output lines.

Truth Table –

As seen from the truth table, the output is 000 when D0 is active; 001 when D1 is active; 010 when D2 is active and so on.

Implementation –
From the truth table, the output line Z is active when the input octal digit is 1, 3, 5 or 7. Similarly, Y is 1 when input octal digit is 2, 3, 6 or 7 and X is 1 for input octal digits 4, 5, 6 or 7. Hence, the Boolean functions would be:

X = D4 + D5 + D6 + D7
Y = D2 +D3 + D6 + D7
Z = D1 + D3 + D5 + D7 

Hence, the encoder can be realised with OR gates as follows:

DECODERS-

A decoder is a combinational circuit that

 converts binary information from 'n' input 

lines to a maximum of 2n unique lines.

BLOCK DIAGRAM FOR 2*4 

TRUTH TABLE-

LOGICAL GATES-

ANOTHER EXAMPLE-

Let’s take an example of 3-to-8 line decoder.
Truth Table –
 
ZRX
Y
Z
D0
D1
D2
D3
D4
D5
D6
D7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1

Implementation –
D0 is high when X = 0, Y = 0 and Z = 0. Hence,
D0 = X’ Y’ Z’ 
Similarly,
D1 = X’ Y’ Z
D2 = X’ Y Z’
D3 = X’ Y Z
D4 = X Y’ Z’
D5 = X Y’ Z
D6 = X Y Z’
D7 = X Y Z 
Hence,