---
title: "4-bit R-2R ladder bit voltages and 1011 output"
subject: "Advanced Electronics"
chapter: 3
key: "semester_4/advanced_electronics:r2r-4bit-12v-1011"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/r2r-4bit-12v-1011
site: BCT Engineering
---

# 4-bit R-2R ladder bit voltages and 1011 output

Advanced Electronics · Chapter 3: Digital-to-Analog and Analog-to-Digital Conversion

- Asked in: 2069 Asar, 2+2+1+2 marks
- Video: [R-2R Ladder Digital to Analog Converter & Advantage।Voltage Switched Network in Digital Electronic](https://www.youtube.com/watch?v=-dpNm8r_hEM) — Oxygen Classes Institute 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/r2r-4bit-12v-1011
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3

## Question

Determine the output voltages caused by each bit in a 4 bit voltage mode R-2R ladder if the input levels are '0' = 0V and '1' = +12V. Determine the resolution and full scale output of this ladder circuit and also find out the voltage from the above ladder for a digital input of 1011.

## Short answer

Each bit contributes: MSB 6 V, 3 V, 1.5 V, and LSB 0.75 V. Resolution is 0.75 V, full-scale output is 11.25 V. For input 1011, the output voltage is 8.25 V.

## Answer

In a 4-bit voltage-mode R-2R ladder, each bit contributes a binary-weighted fraction of the logic-1 voltage at the output. The MSB gives V/2, then V/4, V/8 and V/16. Here logic 1 = +12 V and logic 0 = 0 V.

#### Output due to each bit
```text
Vo = V1 (b3/2 + b2/4 + b1/8 + b0/16),   V1 = 12 V
```

| Bit | Weight | Output when only that bit is 1 |
|---|---|---|
| b3 (MSB) | 1/2 | 12/2 = 6 V |
| b2 | 1/4 | 12/4 = 3 V |
| b1 | 1/8 | 12/8 = 1.5 V |
| b0 (LSB) | 1/16 | 12/16 = 0.75 V |

#### Resolution
The resolution is the output change for 1 LSB:

```text
Resolution = V1 / 2⁴ = 12/16 = 0.75 V
```

#### Full scale output
Full scale output is the output for input 1111:

```text
VFS = 6 + 3 + 1.5 + 0.75 = 11.25 V
    = 12 × 15/16 = 11.25 V
```

#### Output for input 1011
```text
Vo = 6 (b3=1) + 0 (b2=0) + 1.5 (b1=1) + 0.75 (b0=1)
   = 8.25 V
Check: 12 × 11/16 = 8.25 V
```

**Answer:** bit outputs 6 V, 3 V, 1.5 V, 0.75 V; resolution = 0.75 V; full scale = 11.25 V; output for 1011 = **8.25 V**.

## Check yourself

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

1. MSB output with logic 1 = 12 V:
   A. 3 V
   B. 12 V
   C. 0.75 V
   D. 6 V
   Answer: D. MSB weight is 1/2. (Key point: MSB contribution)

2. Resolution of this ladder:
   A. 0.75 V
   B. 1.5 V
   C. 0.8 V
   D. 3 V
   Answer: A. 12/16 = 0.75 V. (Key point: Resolution)

3. Full scale output for 1111:
   A. 12 V
   B. 11.25 V
   C. 9 V
   D. 6.75 V
   Answer: B. 12 x 15/16 = 11.25 V, one LSB below 12 V. (Key point: Full scale)

4. Output for 1011:
   A. 7.5 V
   B. 9.75 V
   C. 8.25 V
   D. 9 V
   Answer: C. 6 + 1.5 + 0.75 = 8.25 V. (Key point: Input 1011)

## Related in Advanced Electronics

- [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
- [Non-inverted R-2R ladder DAC output](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Anon-inverted-r2r-dac) — Advanced Electronics, chapter 3, asked 4×
- [Design 4-bit R-2R DAC; unipolar vs bipolar](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Adesign-4bit-r2r-unipolar-bipolar) — 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
- [Current-mode R-2R preference; bipolar DAC](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Acurrent-mode-r2r-bipolar-dac) — Advanced Electronics, chapter 3
- [Inverted R-2R DAC output and advantages](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverted-r2r-dac-advantages) — Advanced Electronics, chapter 3, asked 4×

## Related in other subjects

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- [TTL input and output signal levels](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Attl-signal-levels) — Digital Logic, chapter 10, asked 2×
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