What does a decoder do?

Converts an n-bit code into one of 2^n output lines

Converts 2^n lines to an n-bit code

In the 3x8 decoder from two 2x4 decoders, what does A do?

It selects which decoder is enabled (A' enables decoder 1 and A enables decoder 2)

It goes to the data inputs of both decoders

2080 Bhadra · 1+4 marks

Decoder; 3×8 decoder from two 2×4 decoders

Short answer

A decoder converts an n-bit input into one active output among 2^n lines. A 3×8 decoder uses two 2×4 decoders with enable: inputs B and C connect to both decoders; A=0 enables decoder1 (D0–D3), A=1 enables decoder2 (D4–D7), using an inverter on A.

What is meant by a decoder? Construct 3×8 decoder using two 2×4 decoders and additional gates if required.

A decoder is a combinational circuit that converts an $n$ -bit binary input code into one of $2^n$ unique output lines; for each input combination exactly one output is active (it generates all minterms).

3×8 decoder using two 2×4 decoders

Let the inputs be $A$ (MSB), $B$ , $C$ (LSB). Each 2×4 decoder has an enable input $E$ (active high).

$B$ and $C$ go to the inputs of both 2×4 decoders.
$A$ selects which decoder works: $A'$ (through a NOT gate) drives $E$ of decoder 1 and $A$ drives $E$ of decoder 2.
When $A = 0$ , decoder 1 is enabled and gives $D_0$ – $D_3$ ; when $A = 1$ , decoder 2 gives $D_4$ – $D_7$ .

                 +---------+
B,C --------+--->| 2x4 #1  |--> D0..D3
            |  +>| E       |
            |  | +---------+
            |  |
A --+-[NOT]-|--+
    |       |    +---------+
    |       +--->| 2x4 #2  |--> D4..D7
    +----------->| E       |
                 +---------+

A	B	C	Active output
0	0	0	$D_0$
0	0	1	$D_1$
0	1	0	$D_2$
0	1	1	$D_3$
1	0	0	$D_4$
1	0	1	$D_5$
1	1	0	$D_6$
1	1	1	$D_7$

Only one extra gate (an inverter) is needed. With an overall enable $E$ , use $E\cdot A'$ and $E\cdot A$ (two AND gates) for the two enables.

✓ Answer checked by Claude Opus 5.5 (high effort)

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