GATE CS 2020 Q.30 (CS Q.20): Combinational Circuits

If there are $m$ input lines and $n$ output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of $m + n$ is _______.

Your answer

Official answer and solution

Official answer: 1034
From: Official GATE 2020 answer key

Solution

Calculate the input address lines m and output select lines n of a decoder for a 1 KB byte-addressable memory.

The memory capacity is $1 \text{ KB} = 1024 \text{ bytes} = 2^{10} \text{ bytes}$ . Because the memory is byte-addressable, there are 1024 unique addressable locations.

A decoder uniquely addresses each byte location by activating exactly one output line for each distinct input address:

Number of output lines: $n = 1024$ .
Number of input lines: $m = \log_2(1024) = 10$ .

The minimum value of $m + n$ is:

m + n = 10 + 1024 = 1034

Final answer

1034

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2020 Computer Science and Information Technology (CS)
Question: 30 of 65, printed as CS Q.20
Section: Computer Science and Information Technology

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