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[Solved]: A Combinational circuit Problem

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Problem Detail: 

A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000, 1 by 0001, …, 9 by 1001. A Combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit $\geq$ 5, and 0 otherwise. If only AND, OR and NOT gates may be used, what is the minimum number of gates required?

My Solution: After analyzing the patterns of the 4 bits ABCD

$\\0000\\ 0001\\ 0010\\ 0011\\ 0100\\ 0101\\ 0110\\ 0111\\ 1000\\ 1001\\$

I've come up with this Combinational Circuit

enter image description here

But it took me 5 gates realzize the given output. I was wondering, can we realize the given output with less number of gates ($<$ 5 gates)

Asked By : Atinesh

Answered By : D.W.

You can solve this problem on your own by writing a program to enumerate all circuits with fewer than 5 gates, and for each one, test whether it has the right truth table. The running time should be minimal, as there aren't that many circuits with fewer than 5 gates.

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