How many AND gates are required for 1-to-8 multiplexer ?
8
A 1-to-8 data selector/distributor (demultiplexer) routes one input line to one of 8 outputs selected by 3 select lines \((2^3 = 8)\).
Each output is produced by one AND gate whose inputs are the data line and one decoded combination of the select lines, for example \(Y_0 = D\,\bar{S_2}\,\bar{S_1}\,\bar{S_0}\), \(Y_7 = D\,S_2 S_1 S_0\).
One AND gate is therefore needed for every output line, i.e. 8 AND gates (plus 3 NOT gates for the complemented select lines). The same count of 8 AND gates applies to an 8-line multiplexer, where the AND outputs are combined by an OR gate.
Hence, the answer is 8.
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