# Question: Enable bit plays an important role in decoder expansions. How is this justified in designing 5X32 line decoder using 2×4 decoders – Free Chegg Question Answer

Enable bit plays an important role in decoder expansions. How is this justified in designing 5X32 line decoder using 2×4 decoders

Transcribed text From Image:

## Expert Chegg Question Answer:

Answer:

## Answer

**The answer as follows :**

A decoder is a combinational circuit that takes n binary inputs and maps them to 2^{n} number outputs. In a 2 × 4 decoder there are 2 (two) inputs and 4 (four) outputs, whereas in a 5 × 32 line decoder there are 5 (five) inputs and 32 (thirty two) outputs where only one is high (enable). So a 5-input decoder there are 2^{5} i.e. 32 outputs. It can be implemented by decoding logic by stages of smaller decoders as well. So, to implement 5 × 32 line decoders, 4 (four) numbers of 3-to-8 (3 × 8) line decoders can be taken to get 32 outputs and each of the four decoders can then be selected through a single 2-to-4 (2 × 4) line decoder.

**It can be implemented in two (stages). Inititially two 2×4 decoders are required for implementing one 3 × 8 decoder in the first (1 ^{st}) stage.**

The block diagram of 3 × 8 decoder using 2×4 decoders is shown in the following figure:

The parallel inputs A1 & A0 are applied to each 2×4 decoder. The complement of input A2 is connected to Enable, E of lower 2 to 4 decoder in order to get the outputs, Y3 to Y0. These are the lower four min terms. The input, A2 is directly connected to Enable, E of upper 2 to 4 decoder in order to get the outputs, Y7 to Y4. These are the higher four min terms. Thus 2 (two) numbers of 2×4 decoders are required to construct each 3 × 8 line decoder.

**Now to implement 5×32 line decoder as shown below: **

Number of inputs (5) : I0 to I4

Enable bit : En

Number of outputs (32) : D0 to D31

**In the second (2 ^{nd}) stage one (01) number of 2×4 line decoder is required with four (04) numbers of 3 × 8 line decoders for selecting each of them, as follows :**

**Fig. 1 : 5 × 32 line decoder using 2 × 4 decoders**

I0, I1 and I2 are the inputs of 3 × 8 decoders, whereas I3 and I4 are the inputs of 2×4 decoders.

En is the enable bit of all the decoders. So, there are 5 (five) number of inputs. Each 3 × 8 decoder has 8 (eight) number of outputs as shown in Fig. 1. Hence, there are 32 (thirty two) number of ouputs from the above 5 number of inputs.

**Therefore, the above Fig.1 thus justified in designing 5 × 32 line decoder using 2 × 4 decoders.**