---
title: "A+B'C to standard minterm form"
subject: "Digital Logic"
chapter: 3
key: "semester_3/digital_logic:standard-minterm-a-plus-bc"
source: https://www.bctengineer.com/q/semester_3/digital_logic/standard-minterm-a-plus-bc
site: BCT Engineering
---

# A+B'C to standard minterm form

Digital Logic · Chapter 3: Combinational Logic Circuits

- Asked in: 2070 Chaitra, 3 marks
- Video: [Converting Boolean Expressions into Standard Form | Sum of Products (SOP) Form](https://www.youtube.com/watch?v=1FUoHJW_am4) — ENGINEERING TUTORIAL
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/standard-minterm-a-plus-bc
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-3

## Question

Convert the following term into standard min term. A+B'C.

## Short answer

Expand A+B'C by adding missing variables: A'B'C + AB'C' + AB'C + ABC' + ABC. The standard minterm form is Σm(1,4,5,6,7).

## Answer

A standard (canonical) minterm form has all variables in every term. Here the variables are A, B, C.

**Step 1: expand each term with the missing variables** using $X + \overline{X} = 1$.

Term $A$ (B and C missing):
$$
\begin{aligned} A &= A(B+\overline{B})(C+\overline{C}) \\ &= ABC + AB\overline{C} + A\overline{B}C + A\overline{B}\,\overline{C} \end{aligned}
$$

Term $\overline{B}C$ (A missing):
$$
\overline{B}C = \overline{B}C(A+\overline{A}) = A\overline{B}C + \overline{A}\,\overline{B}C
$$

**Step 2: add the terms and keep the repeated one only once** ($A\overline{B}C$ appears twice; $X + X = X$):
$$
F = ABC + AB\overline{C} + A\overline{B}C + A\overline{B}\,\overline{C} + \overline{A}\,\overline{B}C
$$

**Step 3: write the minterm numbers**

| Term | ABC | Minterm |
|---|---|---|
| $\overline{A}\,\overline{B}C$ | 001 | $m_1$ |
| $A\overline{B}\,\overline{C}$ | 100 | $m_4$ |
| $A\overline{B}C$ | 101 | $m_5$ |
| $AB\overline{C}$ | 110 | $m_6$ |
| $ABC$ | 111 | $m_7$ |

$$
F = A + \overline{B}C = \Sigma m(1,4,5,6,7)
$$

Check: F = 1 whenever A = 1 (rows 4 to 7) or when B = 0, C = 1 (rows 1 and 5), which gives the same set.

## Check yourself

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

1. How is the missing variable handled when converting a term to minterms?
   A. Multiply by (X + X') for each missing variable X
   B. Add X to the term
   C. Delete the term
   D. Multiply by X only
   Answer: A. Since X + X' = 1, multiplying by it adds the variable without changing the function. (Key point: Expanding missing variables)

2. Expanding the term A in three variables A, B, C gives how many minterms?
   A. 1
   B. 2
   C. 4
   D. 8
   Answer: C. A is missing B and C, so it expands to 2 x 2 = 4 minterms (m4, m5, m6, m7). (Key point: Expansion of A)

3. What is the standard minterm form of A + B'C?
   A. Σm(1,4,5,6,7)
   B. Σm(1,3,5,7)
   C. Σm(4,5,6,7)
   D. Σm(0,1,4,5)
   Answer: A. A gives 4,5,6,7 and B'C gives 1 and 5; with the repeat 5 removed: Σm(1,4,5,6,7). (Key point: Final answer)

## Related in Digital Logic

- [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
- [Canonical form of A(B'+C)+BD; minterm/maxterm](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Acanonical-form-minterm-maxterm) — Digital Logic, chapter 3
- [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
- [Octal-to-binary encoder; A+B'C canonical form](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aoctal-binary-encoder-canonical) — Digital Logic, chapter 4

## Related in other subjects

- [Dynamic equation of GVF, wide rectangular form](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agvf-dynamic-equation-wide-rectangular) — Hydraulics, chapter 8, asked 2×
- [Hyperbola: locus and standard equation](https://www.bctengineer.com/question.md?key=semester_1%2Fmathematics_i%3Ahyperbola-standard-equation-locus) — Mathematics I, chapter 3, asked 6×
- [Derive standard equation of an ellipse](https://www.bctengineer.com/question.md?key=semester_1%2Fmathematics_i%3Aellipse-standard-equation-derive) — Mathematics I, chapter 3, asked 6×
- [Convert and evaluate A/B-(C+D)*E](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Apostfix-evaluate-ab-slash-cd-e) — Data Structure and Algorithm, chapter 2, asked 2×