CUET PG 2021 — Computer PYQ

Q: How do I solve CUET PG 2021 Computer questions?

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Question

CUET PG 2021 — Computer PYQ

CUET PG | Computer | 2021

Don’t care conditions can be used for simplifying Boolean expressions in

Choose the correct answer:

Explanation

The size of a group ( $G$ ) in a K-Map is always a power of 2:

G = 2^n \quad \text{where } n \in \{0, 1, 2, 3, 4\}

If $X$ helps increase $n$ : Include it in the group.
If $X$ does not increase $n$ : Treat it as $0$ and ignore it.

Numerical Example

If we have a function $f(A, B, C, D) = \sum m(1, 3, 7) + \sum d(0, 5)$ :

Step-by-step grouping:

Without Don't Cares: We might only form small pairs.
With Don't Cares ( $0$ and $5$ ): We can form a single Quad (group of 4).

\text{Group} = \{m_1, m_3, d_0, d_2\} \implies \text{Result} = \bar{A}\bar{B}

(Note: Using $d_0$ and $d_2$ eliminates more variables than grouping $m_1$ and $m_3$ alone.)

Final Mathematical Goal

\min(\text{Variables}) \propto \max(\text{Group Size using } X)

K-Map problem