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# Number algebra : Arithmetic Logic Units, Comparators, Decoders, Multiplexers, Demultiplexers and Shifters

1. ALU
Design a 1-bit ALU that can perform add, AND, XOR and NOT operations.
2. Decoders
Design a 4-to-16 decoder using 2-to-4 decoders.
3. Comparators

Design 4-bit comparators that would evaluate the following single relations:
(a) X>Y
(b) X~ Y
4. Multiplexers
Build a 16-to-1 multiplexer using only:
? 4-to-1 multiplexers
? 8-to-1 multiplexers
**Note: multiplexers are sometimes called selectors
5. Demultiplexers
Draw the logic diagram of a 2-bit demultiplexer, a circuit whose single input line is steered to one of the four output lines depending on the state of the two control lines.
6. Shifters
Build an 8-bit right shifter that can shift the input one or two bits to the right, depending on a control input C (if C is 0 then shift right by 1 bit, if C is 1 shift right by 2 bits).

keywords: ALUs

#### Solution Summary

Arithmetic Logic Units, Comparators, Decoders, Multiplexers, Demultiplexers and Shifters are investigated. The solution is detailed and well presented.

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