---
title: "PLA for F1 = Σm(3,5,6,7), F2 = Σm(0,2,4,7)"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:pla-two-functions"
source: https://www.bctengineer.com/q/semester_3/digital_logic/pla-two-functions
site: BCT Engineering
---

# PLA for F1 = Σm(3,5,6,7), F2 = Σm(0,2,4,7)

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2082 Baisakh, 6 marks
- Video: [Programmable Logic Array (PLA) in Digital Electronics || DLD | Implement Boolean functions using PLA](https://www.youtube.com/watch?v=7PQwJQb6OkE) — Sudhakar Atchala
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/pla-two-functions
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

Implement the circuit with a PLA of the following Boolean function: F1 = Σm(3,5,6,7) and F2 = Σm(0,2,4,7).

## Short answer

Minimize: F1 = AB + AC + BC; F2 = A'C' + B'C' + ABC. Program six product terms in PLA: AB, AC, BC, A'C', B'C', ABC. F1 ORs the first three terms; F2 ORs the last three terms.

## Answer

A **PLA** (Programmable Logic Array) has a programmable AND array that forms product terms and a programmable OR array that sums them into outputs. To use it efficiently, each function is minimized and product terms are shared where possible.

#### Simplification

$F_1 = \Sigma m(3,5,6,7)$:

| A \ BC | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 | 1 |

$$
F_1 = AB + AC + BC
$$

$F_2 = \Sigma m(0,2,4,7)$:

| A \ BC | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 |

Groups: (0, 2) gives $A'C'$; (0, 4) gives $B'C'$; 7 alone gives $ABC$.

$$
F_2 = A'C' + B'C' + ABC
$$

#### PLA programming table

Six product terms are needed (none is common to both functions). In the input columns 1 = true variable, 0 = complemented, – = not connected; in the output columns 1 = term connected to that OR gate.

| Term | Product | A | B | C | $F_1$ | $F_2$ |
|---|---|---|---|---|---|---|
| 1 | $AB$ | 1 | 1 | – | 1 | – |
| 2 | $AC$ | 1 | – | 1 | 1 | – |
| 3 | $BC$ | – | 1 | 1 | 1 | – |
| 4 | $A'C'$ | 0 | – | 0 | – | 1 |
| 5 | $B'C'$ | – | 0 | 0 | – | 1 |
| 6 | $ABC$ | 1 | 1 | 1 | – | 1 |

Size: 3 inputs × 6 product terms × 2 outputs.

#### PLA diagram

```text
 A  A' B  B' C  C'        (input buffers)
 |  |  |  |  |  |
 x--+--x--+--+--+--[AND]-- P1 = AB
 x--+--+--+--x--+--[AND]-- P2 = AC
 +--+--x--+--x--+--[AND]-- P3 = BC
 +--x--+--+--+--x--[AND]-- P4 = A'C'
 +--+--+--x--+--x--[AND]-- P5 = B'C'
 x--+--x--+--x--+--[AND]-- P6 = ABC
            OR array
 P1, P2, P3 ----------[OR]--> F1
 P4, P5, P6 ----------[OR]--> F2
 (x = programmed connection)
```

**Check:** $ABC = 110$ (6): $P_1 = 1$, so $F_1 = 1$; $P_4 = P_5 = P_6 = 0$, so $F_2 = 0$. Both match the given minterm lists for all 8 inputs.

## Check yourself

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

1. What defines a PLA compared with other programmable devices?
   A. Only the AND array is programmable
   B. Both the AND array and the OR array are programmable
   C. Only the OR array is programmable
   D. Neither array is programmable
   Answer: B. A PLA forms product terms in a programmable AND array and sums them in a programmable OR array. (Key point: PLA structure)

2. What is the minimised form of F1 = Σm(3,5,6,7)?
   A. AB + C
   B. A + BC
   C. AB + AC + BC
   D. A'B + AC' + BC
   Answer: C. K-map pairs 3 and 7 (BC), 5 and 7 (AC) and 6 and 7 (AB). (Key point: Simplified F1)

3. How many product terms does the PLA need, and why?
   A. Three, because both functions share all terms
   B. Four, because F2 has four minterms
   C. Eight, one per minterm
   D. Six, because no product term is common to both functions
   Answer: D. F1 uses AB, AC, BC and F2 uses A'C', B'C', ABC, none of which are common. (Key point: Product terms)

4. What is the simplified F2 = Σm(0,2,4,7)?
   A. A'C' + B'C' + ABC
   B. A'B' + C'
   C. AB + BC
   D. A'C' + ABC'
   Answer: A. Pairs (0,2) give A'C', (0,4) give B'C' and 7 stands alone as ABC. (Key point: Simplified F2)

## Related in Digital Logic

- [PROM vs PLA; functions using PAL](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aprom-pla-pal-functions) — Digital Logic, chapter 4
- [PLA and full subtractor using PLA](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Apla-full-subtractor) — Digital Logic, chapter 4
- [32:1 MUX tree from 4:1; implement Σ(0,1,3,8,9,13)](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-32to1-tree-function) — Digital Logic, chapter 4
- [32:1 MUX tree; implement Σm(0,1,3,8,9,13,15)](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Amux-32to1-tree-function-15) — Digital Logic, chapter 4
- [RAM vs ROM; functions using PROM](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aram-rom-prom-functions) — Digital Logic, chapter 4
- [ROM and implementing two functions](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Arom-two-functions) — Digital Logic, chapter 4

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