Question

How many 3-line-to-8-line decoders are required for a 1-of-32 decoder?

• A. 4
• B. 2
• C. 1
• D. 8

Hint:

Building Larger Decoders. To get N outputs using decoders with M outputs each, you need N/M decoders for the output stage. Additional logic or decoders may be needed for enable/select lines based on the input address bits.

Answer 1

The Correct Option is A

A 1-of-32 decoder has 32 output lines
It requires \(\log_2(32) = 5\) input lines to select one of the 32 outputs
We want to build this using 3-line-to-8-line decoders
Each 3-to-8 decoder has 8 outputs
To get 32 outputs, we need \( 32 / 8 = 4 \) decoders for the output stage
These 4 decoders can be arranged such that their 8 outputs together form the 32 required outputs
The lower 3 input bits of the 5-bit address can be connected in parallel to the address inputs of all 4 decoders
The higher 2 input bits can be used (possibly with another smaller decoder like a 2-to-4 decoder) to enable only one of the four 3-to-8 decoders at a time, selecting which group of 8 outputs is active
Regardless of the enabling scheme, 4 units of 3-to-8 decoders are fundamentally needed to provide the 32 distinct outputs