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Decoder:-

A decoder is a combinational circuit. It has n input and to a maximum m = 2n outputs. Decoder is identical to a demultiplexer without any data input. It performs operations which are exactly opposite to those of an encoder.

Block diagram:-

Truth table:-

Diagram:-

*formed using simulator.

Encoder:-

Encoder is a combinational circuit which is designed to perform the inverse operation of the decoder. An encoder has n number of input lines and m number of output lines. An encoder produces an m bit binary code corresponding to the digital input number. The encoder accepts an n input digital word and converts it into an m bit another digital word.

Block diagram:-

Truth table:-

Diagram:-

*formed using simulator.

2-Bit Comparator:-

A 2-bit comparator compares two binary numbers, each of two bits and produces their relation such as one number is equal or greater than or less than the other.

Block Diagram:-

The first number A is designated as A = A1A0 and the second number is designated as B = B1B0. This comparator produces three outputs as G (G = 1 if A>B), E (E = 1, if A = B) and L (L = 1 if A<B).

Truth Table:-

K-Map:-

*Solving the equations I got:-

Diagram:-

*formed using simulator provided