Octal (1-of-8) decoder basics – a 1-of-8 decoder asserts one of eight outputs and therefore requires how many binary input bit(s) to select among those outputs?

Introduction / Context: Decoders translate binary input codes into one-of-N outputs. The “octal” or 1-of-8 decoder is a common MSI element used in address selection and control. Determining the number of input bits required is a direct application of the 2^n relationship between inputs and outputs in decoding logic.

Given Data / Assumptions:

• Outputs: 8 distinct lines, exactly one asserted for any valid input.
• Mapping: with n bits, you can represent 2^n states.
• Enable pins may be present but do not add to the selection width.

Concept / Approach: You need enough input bits to index all eight outputs uniquely. Since 2^3 = 8, three input bits are sufficient and necessary. This is why devices such as the 74HC138 are described as “3-to-8 decoders.” The enable inputs control whether any decoding occurs but do not increase the selection count; they simply gate the outputs on or off as a group.

Step-by-Step Solution:

Verification / Alternative check: Any standard 3-to-8 decoder datasheet confirms the mapping and shows enable-controlled output polarity (often active-low outputs).

Why Other Options Are Wrong: Two bits cover only 4 outputs; four bits cover 16 outputs; one bit covers 2 outputs; five bits cover 32 outputs—none match the 8-output case.

Common Pitfalls: Counting enable pins as “inputs” for selection; ignoring active-low conventions that might hide the one-hot nature at first glance.

Final Answer: three