What does an encoder do?

Gives the binary code of the active input line (reverse of a decoder)

Activates one output for each input code

Selects one of many inputs onto one output

What is the role of the first-level decoder with inputs A, B?

Its outputs enable one of the second-level decoders

It produces the final outputs Y0-Y15

It drives C and D for the others

2076 Asoj

Encoder; 4×16 decoder from 2×4 decoders

Short answer

An encoder converts 2^n input lines to n-bit binary code. A 4×16 decoder is built with five 2×4 decoders: one uses inputs A,B to enable one of four second-level decoders, each using C,D to produce 4 outputs, yielding 16 outputs.

Define encoder. Design 4×16 Decoder using 2×4 Decoder only.

An encoder is a combinational circuit that does the reverse of a decoder: it has $2^n$ (or fewer) input lines and $n$ output lines, and gives the binary code of the input line that is active. Example: an 8-to-3 (octal-to-binary) encoder gives $Y_2Y_1Y_0 = 101$ when input $D_5$ is high.

4×16 decoder using only 2×4 decoders

Inputs $A$ (MSB), $B$ , $C$ , $D$ (LSB). Each 2×4 decoder has an enable input $E$ . Five 2×4 decoders are needed, in two levels.

First level (1 decoder): inputs $A$ , $B$ . Its four outputs act as enables, selecting one of the second-level decoders.
Second level (4 decoders): inputs $C$ , $D$ in common. Only the enabled one gives an active output.

                       +-------+
            C,D ------>| 2x4 #1|--> Y0..Y3
                  +--->| E     |
                  |    +-------+
  +--------+  O0--+    +-------+
A-|  2x4   |  O1------>| 2x4 #2|--> Y4..Y7
B-|  (#0)  |  O2--+    +-------+
E-|        |  O3-+|    +-------+
  +--------+     |+--->| 2x4 #3|--> Y8..Y11
                 |     +-------+
                 |     +-------+
                 +---->| 2x4 #4|--> Y12..Y15
                       +-------+
 (C,D go to all four second-level decoders)

AB	Enabled decoder	Outputs active (by CD)
00	#1	$Y_0$ – $Y_3$
01	#2	$Y_4$ – $Y_7$
10	#3	$Y_8$ – $Y_{11}$
11	#4	$Y_{12}$ – $Y_{15}$

Example: $ABCD = 1101$ : decoder #0 makes O3 high, enabling #4; $CD = 01$ makes its second output high, so $Y_{13} = 1$ (since $1101_2 = 13$ ).

✓ Answer checked by Claude Opus 5.5 (high effort)

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