---
title: "Simplify two expressions and draw circuits"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:simplify-and-draw-circuits"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/simplify-and-draw-circuits
site: BCT Engineering
---

# Simplify two expressions and draw circuits

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2067 Mangsir, 6 marks
- Video: [Example Problems Boolean Expression Simplification](https://www.youtube.com/watch?v=0as464WmfCo) — ENGRTUTOR
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/simplify-and-draw-circuits
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Simplify the expressions and draw the circuits. i) A'B'C' + A'B'C + AB'C' + AB'C  ii) AC' + ABC + A(C + AC')

## Short answer

i) A'B'C' + A'B'C + AB'C' + AB'C simplifies to B', needing only a NOT gate. ii) AC' + ABC + A(C+AC') simplifies to A, requiring no gate, just a wire.

## Answer

#### i) A'B'C' + A'B'C + AB'C' + AB'C

Group terms with B' common:

```text
= B'(A'C' + A'C + AC' + AC)
= B'[A'(C' + C) + A(C' + C)]
= B'[A' + A]
= B'
```

**Answer: F = B'**

Circuit: only one NOT gate (inverter) with input B.

```text
 B ---[NOT]--- F = B'
```

#### ii) AC' + ABC + A(C + AC')

```text
A(C + AC') = AC + AAC' = AC + AC'
So: AC' + ABC + AC + AC'
  = AC' + ABC + AC            (AC' + AC' = AC')
  = A(C' + C) + ABC
  = A + ABC
  = A(1 + BC)
  = A
```

**Answer: F = A**

Circuit: a direct connection, with no gate. The output follows A.

```text
 A ----------------- F = A
```

Both circuits show how Boolean algebra removes gates: the original needed several AND, OR and NOT gates, but the simplified forms need one NOT gate and a plain wire.

## Check yourself

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

1. In part i, A'B'C' + A'B'C + AB'C' + AB'C is simplified by:
   A. Taking B' common and using (C' + C) = 1 and (A' + A) = 1
   B. Taking A common and using A + A' = 0
   C. Adding all terms
   D. Using the consensus theorem on A and C
   Answer: A. The answer states this: Taking B' common and using (C' + C) = 1 and (A' + A) = 1. (Key point: Part i method)

2. The result of part i is:
   A. B
   B. B'
   C. A'
   D. AB'
   Answer: B. The answer states this: B'. (Key point: Part i result)

3. AC' + ABC + A(C + AC') simplifies to:
   A. AC
   B. AB
   C. A
   D. A + BC
   Answer: C. The answer states this: A. (Key point: Part ii result)

4. The circuit for F = A needs:
   A. One AND gate
   B. One NOT gate
   C. One OR gate
   D. A direct connection, no gate
   Answer: D. The answer states this: A direct connection, no gate. (Key point: Circuit for part ii)

## Related in Basic Electronics Engineering

- [Output waveforms of two diode circuits](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Adiode-circuits-output-waveforms) — Basic Electronics Engineering, chapter 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: 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: two 3-variable functions](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Akmap-two-expressions) — Basic Electronics Engineering, chapter 6

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