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

# K-map: A'BC' + ABC' + ABC

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2071 Bhadra, 3 marks
- 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-three-term
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Simplify the expression using K-map, Y = A'BC' + ABC' + ABC.

## Short answer

Y = Σm(2,6,7): pair (m2,m6) gives BC', pair (m6,m7) gives AB. Simplified: Y = AB + BC'.

## Answer

Y = A'BC' + ABC' + ABC = m2 + m6 + m7 = Σm(2, 6, 7).

#### K-map

```text
          BC
        00  01  11  10
 A = 0 | 0 | 0 | 0 | 1 |
 A = 1 | 0 | 0 | 1 | 1 |
```

Groups:
- Pair (m2, m6): B = 1, C = 0 gives **BC'**.
- Pair (m6, m7): A = 1, B = 1 gives **AB**.

**Answer: Y = AB + BC'**

## Check yourself

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

1. A'BC' + ABC' + ABC equals:
   A. Sigma m(2, 6, 7)
   B. Sigma m(2, 5, 7)
   C. Sigma m(2, 3, 7)
   D. Sigma m(1, 6, 7)
   Answer: A. The answer states this: Sigma m(2, 6, 7). (Key point: Minterm list)

2. The pair (m2, m6) gives:
   A. AB
   B. BC'
   C. AC'
   D. A'B
   Answer: B. The answer states this: BC'. (Key point: Pair (m2, m6))

3. The pair (m6, m7) gives:
   A. BC
   B. BC'
   C. AB
   D. AC
   Answer: C. The answer states this: AB. (Key point: Pair (m6, m7))

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

## Related in Basic Electronics Engineering

- [K-map: A'B + BC' + AC'](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-abc-simple) — Basic Electronics Engineering, chapter 6, asked 2×
- [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

## Related in other subjects

- [SOP/POS forms and canonical form of A+BC+ABC](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Asop-pos-canonical-form) — Digital Logic, chapter 3
- [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×
- [K-map Σm(7,9,12,13,14,15)+d, NOR-only](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-nor-sum-7-9-12) — Digital Logic, chapter 3