2076 Asoj · 3 marks

1×16 DMUX using 1×4 DMUX

Short answer

Use five 1×4 demuxes in a tree. The first demux uses select bits S3S2 to route data D to one of four second-level demuxes, which use S1S0 to select the final output from Y0–Y15. No extra gates needed.

Realize the logic circuit of 1×16 DMUX using 1×4 DMUX and gates if necessary.

A 1×16 DMUX needs 4 select lines $S_3S_2S_1S_0$ . It is built as a demultiplexer tree from five 1×4 DMUXes; no extra gates are needed.

Stage 1: one 1×4 DMUX receives the data $D$ and uses the MSBs $S_3S_2$ to send it to one of four second-stage DMUXes.
Stage 2: four 1×4 DMUXes use $S_1S_0$ and produce $Y_0$ – $Y_{15}$ .

                       S1 S0
                     +------+-- Y0..Y3
         S3 S2    +->| DM1  |
       +------+   |  +------+
  D -->| DM0 0|---+  +------+-- Y4..Y7
       |     1|----->| DM2  |
       |     2|---+  +------+
       |     3|-+ |  +------+-- Y8..Y11
       +------+ | +->| DM3  |
                |    +------+
                |    +------+-- Y12..Y15
                +--->| DM4  |
                     +------+

$S_3S_2$	Active stage-2 DMUX	Outputs reached by $S_1S_0$
00	DM1	$Y_0$ – $Y_3$
01	DM2	$Y_4$ – $Y_7$
10	DM3	$Y_8$ – $Y_{11}$
11	DM4	$Y_{12}$ – $Y_{15}$

Example: $S = 1110$ → DM0 picks DM4, DM4 picks its output 2, so $D$ appears at $Y_{14}$ .

✓ Answer checked by Claude Opus 5.5 (high effort)

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1×16 DMUX using 1×4 DMUX

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