How many 3-to-8 line decoders with an enable input are needed to construct a…

Solution: build a two-level decoder using 3-to-8 decoders with enable inputs.

Key idea: split the 6 input bits into upper three bits and lower three bits.

• Use one 3-to-8 decoder to decode the upper three bits. Its eight outputs serve as enable signals.

• Use eight 3-to-8 decoders for the lower three bits. Connect the same three lower input bits to each of these decoders, and connect each decoder's enable input to a different output of the upper decoder.

• Each enabled lower-stage decoder produces 8 outputs, so the eight decoders together produce 8 × 8 = 64 distinct outputs.

Total decoders required: one upper 3-to-8 decoder + eight lower 3-to-8 decoders = 9 decoders.

Answer: 9 decoders.