A combinational circuit is specified by the following three boolean functions. implement the circuit with $3 \times 8$ decoder constructed with NAND gates and three external NAND or AND gates. Use a block diagram for the decoder. Minimize the number of input in the external gates.
$F _1(A,B,C) = \sum(2,4,7)$
$F _2(A,B,C) = \sum(0,3)$
$F _3(A,B,C) = \sum(0,2,3,4,7)$
