---
title: "K-map: A'B + BC' + AC'"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:kmap-abc-simple"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/kmap-abc-simple
site: BCT Engineering
---

# K-map: A'B + BC' + AC'

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2075 Baisakh, 4 marks; 2068 Magh, 3 marks (asked 2 times)
- Video: [Boolean Expression Solving using K-Map](https://www.youtube.com/watch?v=ewkhVRIzsN0) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/kmap-abc-simple
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Simplify the expression using K-Map, F(A,B,C) = A'B + BC' + AC'.

## Short answer

F(A,B,C) = A'B + BC' + AC' simplifies to A'B + AC'. Using a Karnaugh map, the minterms Σm(2,3,4,6) are grouped into two prime implicants: A'B (covers m2,m3) and AC' (covers m4,m6).

## Answer

Given F(A,B,C) = A'B + BC' + AC'. Expand to minterms:
- A'B = A'BC' + A'BC = m2 + m3
- BC' = A'BC' + ABC' = m2 + m6
- AC' = ABC' + AB'C' = m6 + m4

So F = Σm(2, 3, 4, 6).

#### K-map

```text
          BC
        00  01  11  10
 A = 0 | 0 | 0 | 1 | 1 |     m2, m3 -> A'B
 A = 1 | 1 | 0 | 0 | 1 |     m4, m6 -> AC'
```

Groups:
- Pair (m2, m3): B = 1, C varies, A = 0 gives **A'B**.
- Pair (m4, m6): A = 1, C = 0, B varies gives **AC'**.
- The pair (m2, m6) = BC' is redundant, because both its minterms are already covered.

**Answer: F = A'B + AC'**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. F = A'B + BC' + AC' equals:
   A. Sigma m(2, 3, 4, 6)
   B. Sigma m(1, 3, 4, 6)
   C. Sigma m(2, 3, 5, 6)
   D. Sigma m(0, 2, 3, 4)
   Answer: A. The answer states this: Sigma m(2, 3, 4, 6). (Key point: Minterm list)

2. The pair (m2, m3) gives the term:
   A. BC'
   B. A'B
   C. AC'
   D. A'C
   Answer: B. The answer states this: A'B. (Key point: Group (m2, m3))

3. Why is the group (m2, m6) = BC' redundant?
   A. It covers no 1s
   B. It is not a valid group of two
   C. Both its minterms are already covered by other groups
   D. It contains a 0
   Answer: C. The answer states this: Both its minterms are already covered by other groups. (Key point: Redundant group)

4. The simplified result is:
   A. F = A'B + BC'
   B. F = BC' + AC'
   C. F = A'B + BC' + AC'
   D. F = A'B + AC'
   Answer: D. The answer states this: F = A'B + AC'. (Key point: Final answer)

## Related in Basic Electronics Engineering

- [K-map: A'BC' + ABC' + ABC](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-abc-three-term) — Basic Electronics Engineering, chapter 6
- [K-map: 3-variable five-term expression](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-xyz-five-term) — Basic Electronics Engineering, chapter 6
- [Simplify two expressions and draw circuits](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Asimplify-and-draw-circuits) — Basic Electronics Engineering, chapter 6
- [K-map: x'yz + x'y'z + xyz with gates](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-xyz-realize-gates) — Basic Electronics Engineering, chapter 6, asked 2×
- [K-map: 4-variable minterm list](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-4var-sigma) — Basic Electronics Engineering, chapter 6
- [K-map and universal gate: xy + x'z + yz](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-universal-gate-xy) — Basic Electronics Engineering, chapter 6

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- [K-map Σ(1,2,3,8,10,13)+d, standard SOP](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-standard-sop-123810) — Digital Logic, chapter 3, asked 2×
- [K-map Π(0,4,5,8,9,11,15), standard SOP](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-maxterm-sop-0458) — Digital Logic, chapter 3, asked 2×