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 CircuitBut 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)
A Combinational circuit Problem
boolean algebra;combinatory logic
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.