---
title: "K-map: 4-variable minterm list"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:kmap-4var-sigma"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/kmap-4var-sigma
site: BCT Engineering
---

# K-map: 4-variable minterm list

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2074 Bhadra, 4 marks
- Video: [Lec -13: 4 Variable K-Map with examples | Design K-Map | Minimization in Digital Electronics](https://www.youtube.com/watch?v=0vEvpcY8O3o) — Gate Smashers
- 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-4var-sigma
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Simplify an expression F(A,B,C,D) = Σ(1,3,7,9,11,14,15) by using K-map.

## Short answer

K-map grouping: quad (m1,m3,m9,m11) gives B'D; quad (m3,m7,m11,m15) gives CD; pair (m14,m15) gives ABC. Simplified expression: F = B'D + CD + ABC.

## Answer

F(A,B,C,D) = Σm(1, 3, 7, 9, 11, 14, 15).

#### K-map

```text
           CD
         00  01  11  10
 AB=00 | 0 | 1 | 1 | 0 |
 AB=01 | 0 | 0 | 1 | 0 |
 AB=11 | 0 | 0 | 1 | 1 |
 AB=10 | 0 | 1 | 1 | 0 |
```

#### Groups

1. Quad (m1, m3, m9, m11): B = 0, D = 1 gives **B'D**.
2. Quad (m3, m7, m11, m15): C = 1, D = 1 gives **CD**.
3. Pair (m14, m15): A = 1, B = 1, C = 1 gives **ABC**.

All 7 minterms are covered, and each group is needed (m1, m9 only in group 1; m7 only in group 2; m14 only in group 3).

**Answer: F = B'D + CD + ABC**

## Check yourself

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

1. The quad (m1, m3, m9, m11) gives:
   A. B'D
   B. CD
   C. BD
   D. A'D
   Answer: A. The answer states this: B'D. (Key point: Quad (m1, m3, m9, m11))

2. The quad (m3, m7, m11, m15) gives:
   A. B'D
   B. CD
   C. AD
   D. BC
   Answer: B. The answer states this: CD. (Key point: Quad (m3, m7, m11, m15))

3. The pair (m14, m15) gives:
   A. ABD
   B. BCD
   C. ABC
   D. AB'C
   Answer: C. The answer states this: ABC. (Key point: Pair (m14, m15))

4. The simplified function is:
   A. F = B'D + CD
   B. F = B'D + AB + CD
   C. F = BD + CD + ABC
   D. F = B'D + CD + ABC
   Answer: D. The answer states this: F = B'D + CD + ABC. (Key point: Final answer)

## Related in Basic Electronics Engineering

- [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
- [K-map: two 3-variable functions](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-two-expressions) — Basic Electronics Engineering, chapter 6
- [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: 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: 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 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

- [K-map Σ(0,1,4,8,10,11,12)+d, standard minterm](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-standard-minterm-01248) — Digital Logic, chapter 3
- [K-map Σm(0,1,2,8,10,14,15)+d, POS with NOR](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-pos-nor-0128) — Digital Logic, chapter 3
- [K-map Σ(1,2,3,8,9,10,11,13,14)+d, POS](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-pos-form-12389) — Digital Logic, chapter 3
- [K-map Σ(1,2,3,8,9,10,11,14)+d(0,4,12), NAND](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Akmap-nand-1238-dc-0412) — Digital Logic, chapter 3, asked 5×