---
title: "8-bit DAC LSB, MSB, resolution, full scale"
subject: "Instrumentation II"
chapter: 4
key: "semester_5/instrumentation_ii:dac-lsb-msb-resolution"
source: https://www.bctengineer.com/q/semester_5/instrumentation_ii/dac-lsb-msb-resolution
site: BCT Engineering
---

# 8-bit DAC LSB, MSB, resolution, full scale

Instrumentation II · Chapter 4: Interfacing A/D And D/A Converters

- Asked in: 2071 Chaitra, 2 marks
- Video: [Digital to Analog Converter (DAC) Solved Problem | Quiz # 397](https://www.youtube.com/watch?v=aTnPRK3OuV8) — ALL ABOUT ELECTRONICS - Quiz
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/instrumentation_ii/dac-lsb-msb-resolution
- Whole chapter: https://www.bctengineer.com/md/semester_5/instrumentation_ii/chapter-4

## Question

Calculate the values of the LSB, MSB, resolution and full-scale output for an 8-bit DAC for the 0 to 10V range.

## Short answer

LSB = 10V/256 = 39.06 mV, MSB = 10V/2 = 5 V, resolution = 1/256 = 0.39% (8 bits), full-scale output = 10V × 255/256 = 9.96 V.

## Answer

For an n-bit DAC with full-scale range FSR = 10 V (0 to 10 V), n = 8, number of steps 2^8 = 256.

```text
 LSB (step size) = FSR / 2^n = 10 / 256 = 0.0391 V = 39.06 mV
 MSB weight      = FSR / 2   = 10 / 2   = 5 V
 Resolution      = 1 / 2^n   = 1 / 256 = 0.39 %  (8 bits)
 Full-scale output = FSR x (2^n - 1) / 2^n = 10 x 255 / 256 = 9.961 V
```
(If the DAC is scaled so that the last code gives exactly 10 V, the step is 10/255 = 39.2 mV.)

**Answer: LSB = 39.06 mV, MSB = 5 V, resolution = 8 bits (0.39 % or 1 part in 256), full-scale output = 9.96 V (10 V - 1 LSB).**

## Check yourself

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

1. What is the LSB (step size) of an 8-bit DAC with 0 to 10 V range?
   A. 10/255 = 39.2 V
   B. 10/256 = 39.06 mV
   C. 10/8 = 1.25 V
   D. 10/512 = 19.5 mV
   Answer: B. LSB = FSR / 2^n = 10/256 = 39.06 mV. (Key point: LSB value)

2. What is the MSB weight of this DAC?
   A. 5 V
   B. 2.5 V
   C. 10 V
   D. 39 mV
   Answer: A. MSB weight = FSR/2 = 5 V. (Key point: MSB weight)

3. What is the full-scale output FSR x (2^n - 1)/2^n?
   A. 10 V
   B. 9.5 V
   C. 10.04 V
   D. 9.961 V
   Answer: D. 10 x 255/256 = 9.961 V, i.e. 10 V minus 1 LSB. (Key point: Full-scale output)

## Related in Instrumentation II

- [Interfacing 10-bit DAC with 8085](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac10-8085) — Instrumentation II, chapter 4, asked 2×
- [12-bit DAC with 8085](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac12-with-8085) — Instrumentation II, chapter 4, asked 2×
- [10-bit DAC triangular wave at 500 Hz](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac10-triangular-500hz) — Instrumentation II, chapter 4
- [Interfacing 1408 DAC for 0 to 10 V](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Adac1408-0-10v) — Instrumentation II, chapter 4
- [Bit rate, baud rate and character time at 9600](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Abaud-time-engineer) — Instrumentation II, chapter 3

## Related in other subjects

- [Bipolar DAC output and 3-bit transfer curve](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Abipolar-dac-transfer-curve) — Advanced Electronics, chapter 3
- [5-bit R-2R DAC output for 10110](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ar2r-5bit-10110) — Advanced Electronics, chapter 3
- [4-bit R-2R ladder bit voltages and 1011 output](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ar2r-4bit-12v-1011) — Advanced Electronics, chapter 3
- [4-bit inverted R-2R DAC and why better](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverted-r2r-4bit-better) — Advanced Electronics, chapter 3