GATE CS 2014 Set 1 — Question 17
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumBoolean Laws & TheoremsBoolean Algebra & Logic GatesDigital LogicSOP & POS Forms
Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
Last updated
Question
Consider the following Boolean expression for :The minimal sum-of-products form of is
Correct answer
(A) PQ + QR + QS
Solution
Given Boolean expression:
Factor out :
Using the absorption law on the first two terms inside the parentheses:
So,
Rearrange terms:
Apply again where and :
So,
Apply again where and :
So,
Expanding the expression:
This is the minimal sum-of-products form.
Factor out :
Using the absorption law on the first two terms inside the parentheses:
So,
Rearrange terms:
Apply again where and :
So,
Apply again where and :
So,
Expanding the expression:
This is the minimal sum-of-products form.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Boolean Algebra & Logic Gates
2026 Set 2 Q16Which one of the following options is not a property of Boolean Algebra? Note: is OR…2026 Set 1 Q21Consider the following Boolean expression of a function :…2026 Set 1 Q22Consider the 8-bit signed integers and represented using the sign-magnitude form. The…2026 Set 2 Q28In a system, numbers are represented using 4-bit two’s complement form. Consider four numbers…2026 Set 2 Q34The 32-bit IEEE 754 single precision representation of a number is . The number…