---
title: "Priority encoder; \"e\" and \"f\" segments"
subject: "Digital Logic"
chapter: 4
key: "semester_3/digital_logic:priority-encoder-e-f-segments"
source: https://www.bctengineer.com/q/semester_3/digital_logic/priority-encoder-e-f-segments
site: BCT Engineering
---

# Priority encoder; "e" and "f" segments

Digital Logic · Chapter 4: Data Processing Circuits

- Asked in: 2081 Baisakh, 2+3+3 marks
- Video: [Priority Encoder](https://www.youtube.com/watch?v=kEj-m3YuGa4) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/priority-encoder-e-f-segments
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-4

## Question

What is a priority encoder? Find out the simplest logic circuit for "e" and "f" segments of the BCD-to-seven segment display decoder.

## Short answer

A priority encoder outputs the code of the highest active input. Segment e: e = D'(B' + C) using one OR, two NOT, and one AND. Segment f: f = A + C'D' + BC' + BD' implemented with AND and OR gates.

## Answer

#### Priority encoder

A **priority encoder** is an encoder that gives the binary code of the **highest-priority** active input when more than one input is active at the same time. It also has a valid output $V$ that shows at least one input is active. Example: in a 4:2 priority encoder with $D_3$ highest, if $D_1$ and $D_2$ are both 1, the output is $10$ (code of $D_2$). The 74148 is an 8:3 priority encoder used for interrupt handling and keyboard encoding.

#### Segment "e"

Segment e is ON for digits 0, 2, 6, 8 (inputs 10–15 are don't-cares).

$$
e = \Sigma m(0,2,6,8) + d(10\text{–}15)
$$

| AB \ CD | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 1 | 0 | 0 | 1 |
| 01 | 0 | 0 | 0 | 1 |
| 11 | X | X | X | X |
| 10 | 1 | 0 | X | X |

Groups: corners (0, 2, 8, 10) give $B'D'$; column 10 (2, 6, 10, 14) gives $CD'$.

$$
e = B'D' + CD' = D'(B' + C)
$$

```text
 B --[NOT]--+
            +--[OR]--+
 C ---------+        +--[AND]--- e
 D --[NOT]-----------+
```

#### Segment "f"

Segment f is ON for digits 0, 4, 5, 6, 8, 9.

$$
f = \Sigma m(0,4,5,6,8,9) + d(10\text{–}15)
$$

| AB \ CD | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 1 | 0 | 0 | 0 |
| 01 | 1 | 1 | 0 | 1 |
| 11 | X | X | X | X |
| 10 | 1 | 1 | X | X |

Groups: rows 11 and 10 give $A$; column 00 gives $C'D'$; cells 4, 5, 12, 13 give $BC'$; cells 4, 6, 12, 14 give $BD'$.

$$
f = A + C'D' + BC' + BD'
$$

```text
 C' -+-[AND]-- C'D' --+
 D' -+                |
 B  -+-[AND]-- BC' ---+
 C' -+                +--[OR 4]--- f
 B  -+-[AND]-- BD' ---+
 D' -+                |
 A  ------------------+
```

Both circuits are checked against the digit table: e.g. for digit 6 ($0110$): $e = 0 + 1\cdot1 = 1$ and $f = 0 + 0 + 0 + 1 = 1$, both segments lit as required.

## Check yourself

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

1. In a 4:2 priority encoder with D3 highest, D1 and D2 are both 1. What is the output?
   A. 01
   B. 10
   C. 11
   D. 00
   Answer: B. The highest active input D2 is encoded, giving 10. (Key point: Priority encoder)

2. What is the simplest expression for segment e?
   A. B'D' + CD' = D'(B' + C)
   B. B'D + CD
   C. B + C'D'
   D. D'(B + C)
   Answer: A. Corners give B'D' and column 10 gives CD'. (Key point: Segment e)

3. Segment e is ON for which digits?
   A. 0, 2, 6, 8
   B. 1, 3, 5, 7
   C. 0, 4, 5, 6
   D. 2, 3, 4, 9
   Answer: A. Segment e (lower left) is lit for 0, 2, 6 and 8 among the BCD digits. (Key point: Segment e digits)

4. What is segment f?
   A. A + C'D' + BC' + BD'
   B. A + CD + B
   C. A' + C'D
   D. BC + A
   Answer: A. Groups give A, C'D', BC' and BD' from the K-map with don't-cares. (Key point: Segment f)

## Related in Digital Logic

- [BCD-to-seven-segment decoder, segments a and e](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Abcd-seven-segment-a-e) — Digital Logic, chapter 4
- [DEMUX vs decoder; seven-segment "b" segment](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademux-decoder-b-segment) — Digital Logic, chapter 4
- [Seven-segment decoder "b" segment](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ab-segment-seven-segment) — Digital Logic, chapter 4, asked 2×
- [Seven-segment "b" and "d" segments](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ab-d-segments) — Digital Logic, chapter 4
- [BCD-to-7-segment decoder; frequency counter](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Abcd-7segment-frequency-counter) — Digital Logic, chapter 11
- [Seven-segment "a" segment using NOR gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aa-segment-nor-gates) — Digital Logic, chapter 4

## Related in other subjects

- [Seven segment display and clock counter](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aseven-segment-clock-design) — Embedded System, chapter 9
- [BCD counter 0-9999 on seven segment VHDL](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Avhdl-bcd-counter-seven-segment) — Embedded System, chapter 9
- [Display 99 to 00 on seven segment](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3A8051-seven-segment-99-00) — Embedded System, chapter 9
- [Display 0 to 9 on seven segment](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3A8051-seven-segment-0-9) — Embedded System, chapter 9, asked 2×