GATE CS 2020 Q20 — Combinational Circuits

To uniquely address a byte-addressable memory, each byte location must be mapped to a unique output line of the decoder.

Given:

• RAM size = $1\text{ KB} = 1024\text{ bytes}$
• Since the RAM is byte-addressable, there are $1024$ unique memory locations.

For a decoder to uniquely address these $1024$ locations:

• The number of output lines, $n = 1024$.
• The number of input lines, $m$, must satisfy $2^m \ge n$.

For the minimum value of $m$:

Thus, the minimum value of $m + n$ is: