---
title: "Maxterm with example"
subject: "Digital Logic"
chapter: 3
key: "semester_3/digital_logic:maxterm-explain"
source: https://www.bctengineer.com/q/semester_3/digital_logic/maxterm-explain
site: BCT Engineering
---

# Maxterm with example

Digital Logic · Chapter 3: Combinational Logic Circuits

- Asked in: 2074 Chaitra, 3 marks
- Video: [Minterms(SOP) & Maxterms(POS) | Boolean Algebra](https://www.youtube.com/watch?v=TMxMPJeJ_18) — Simple Snippets
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/maxterm-explain
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-3

## Question

What do you mean by Max term? Explain with example.

## Short answer

A maxterm is an OR term that includes every variable exactly once, in true or complemented form, and is 0 for exactly one input combination. For example, for variables A,B,C, maxterm M2 = A+B'+C is 0 only when A=0,B=1,C=0.

## Answer

A **maxterm** is a sum (OR) term that contains all the variables of the function exactly once, each either in true or complemented form. A maxterm is 0 for exactly one input combination and 1 for all others.

**How to write a maxterm:** for the input combination that should give 0, write a variable as it is if its value is 0, and complemented if its value is 1. Maxterm $M_i$ is the one that is 0 at decimal input $i$.

For three variables A, B, C:

| A B C | Maxterm | Symbol |
|---|---|---|
| 0 0 0 | $A+B+C$ | $M_0$ |
| 0 0 1 | $A+B+\overline{C}$ | $M_1$ |
| 0 1 0 | $A+\overline{B}+C$ | $M_2$ |
| 0 1 1 | $A+\overline{B}+\overline{C}$ | $M_3$ |
| 1 0 0 | $\overline{A}+B+C$ | $M_4$ |
| 1 0 1 | $\overline{A}+B+\overline{C}$ | $M_5$ |
| 1 1 0 | $\overline{A}+\overline{B}+C$ | $M_6$ |
| 1 1 1 | $\overline{A}+\overline{B}+\overline{C}$ | $M_7$ |

Each maxterm is the complement of the minterm with the same number: $M_i = \overline{m_i}$.

**Example:** let F be 0 only for inputs 000, 010 and 101. The function is the AND (product) of the maxterms for these rows (the canonical POS form):
$$
\begin{aligned} F &= M_0 \cdot M_2 \cdot M_5 = \Pi M(0,2,5) \\ &= (A+B+C)(A+\overline{B}+C)(\overline{A}+B+\overline{C}) \end{aligned}
$$

Check: for input 010, the second factor $A+\overline{B}+C = 0+0+0 = 0$, so F = 0. For any other input not in the list, all three factors are 1, so F = 1.

## Check yourself

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

1. Which statement defines a maxterm correctly?
   A. An AND term with all variables that is 1 for exactly one input combination
   B. An OR term with all variables that is 0 for exactly one input combination
   C. An OR term with all variables that is 1 for exactly one input combination
   D. An AND term with some variables that is 0 for one combination
   Answer: B. A maxterm is a sum term containing every variable once and is 0 for exactly one combination. (Key point: Definition of maxterm)

2. For input ABC = 101, how is the maxterm M5 written?
   A. A + B' + C
   B. A' + B + C'
   C. A' + B' + C
   D. A + B + C
   Answer: B. In a maxterm a variable is complemented if its value is 1, so 101 gives A' + B + C'. (Key point: Writing a maxterm)

3. If F is 0 only for inputs 000, 010 and 101, which expression is F?
   A. M0 + M2 + M5
   B. m0 · m2 · m5
   C. M0 · M2 · M5
   D. m0 + m2 + m5
   Answer: C. F is the AND of the maxterms for the 0 rows: F = M0·M2·M5 = ΠM(0,2,5). (Key point: Canonical POS)

## Related in Digital Logic

- [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

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- [Max and min word occurrence with MapReduce](https://www.bctengineer.com/question.md?key=semester_8%2Fbig_data_technologies%3Amapreduce-max-min-word-occurrence) — Big Data Technologies, chapter 3