design a 4 bit comparator that compares two numbers of 4 bits. the output should be...

design a 4 bit comparator that compares two numbers of 4 bits. the output should be < > or =. however you're only limited to using multiplexers or full adders. any help on how to draw this will be appreciated

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Expert Solution

The truth table of the 4bit comparator is given below

In order to implement the above circuit with fewer gates, we modify the circuit that is shown in the following figure

In order to reduce the area, we can still decrease the number of gates. The logic of A<B can be decided by A>B and A=B, so we can simplify the above circuit as below. 2-input NOR is used here to realize the function of A<B.The area of 2-input NOR is much less than that of G11~G15. On the other hand, fewer gates means fewer power, so this modification can greatly reduce the power dissipation. Therefore, the logic optimization is completed.

genius_generous answered 1 year ago

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