1) A combinational circuit is specified by the following three Boolean functions:
a) $F_1(A, B, C) = \sum_{m}(1, 4, 6)$
b) $F_2(A, B, C) = \sum_{m}(3, 5)$
c) $F_3(A, B, C) = \sum_{m}(2, 4, 6, 7)$
Implement the circuit with a decoder constructed with NAND gates connected to the decoder outputs. Use a block diagram for the decoder. Minimize the number of inputs in the external gates.