---
title: "5-bit R-2R DAC output for 10110"
subject: "Advanced Electronics"
chapter: 3
key: "semester_4/advanced_electronics:r2r-5bit-10110"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/r2r-5bit-10110
site: BCT Engineering
---

# 5-bit R-2R DAC output for 10110

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

- Asked in: 2071 Chaitra, 4+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/r2r-5bit-10110
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-3

## Question

Draw a circuit diagram for 5 bit R-2R (voltage type) DAC. If the reference voltage for the DAC is 1V, the binary input is 10110, find the output voltage.

## Short answer

The 5-bit R-2R ladder output is Vo = Vref * D/32 where D is the decimal value of the binary input. For input 10110 (D=22) and Vref=1V, Vo = 1 * 22/32 = 0.6875 V.

## Answer

A 5-bit voltage-mode R-2R ladder DAC uses resistors R and 2R only. Each bit switches its 2R leg to Vref (bit 1) or ground (bit 0). The output is taken at the MSB end of the ladder through a buffer.

#### Circuit
```text
 Vo<-+----R----+----R----+----R----+----R----+
     |         |         |         |         |
     2R        2R        2R        2R        2R     2R
     |         |         |         |         |      |
    b4        b3        b2        b1        b0     GND
   (MSB)                                  (LSB)
  each switch: 1 -> Vref, 0 -> GND
  Vo -> voltage follower (op-amp) -> Vout
```

#### Output relation
Each bit adds a binary-weighted part of Vref (MSB gives Vref/2, the next Vref/4, and so on):

```text
Vo = Vref (b4/2 + b3/4 + b2/8 + b1/16 + b0/32)
   = Vref · D / 2⁵
```

#### Calculation for input 10110, Vref = 1 V
```text
D  = 1·16 + 0·8 + 1·4 + 1·2 + 0·1 = 22
Vo = 1 V × 22/32
   = 1 × (1/2 + 1/8 + 1/16)
   = 0.5 + 0.125 + 0.0625
   = 0.6875 V
```

**Answer:** Vo = **0.6875 V** with a unity-gain buffer.

Resolution of this DAC = 1/32 = 31.25 mV. Full-scale output = 31/32 = 0.96875 V.

(If the ladder output drives an inverting amplifier of gain −1, the output is −0.6875 V. The magnitude is the same.)

## Check yourself

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

1. The output of a 5-bit voltage-mode R-2R DAC is:
   A. Vo = Vref D/2^5
   B. Vo = Vref D/2^4
   C. Vo = Vref D x 32
   D. Vo = Vref/D
   Answer: A. Each bit adds a binary-weighted part Vref/2, Vref/4, ... Vref/32. (Key point: Formula)

2. The decimal value of 10110 is:
   A. 26
   B. 22
   C. 13
   D. 11
   Answer: B. 16 + 4 + 2 = 22. (Key point: Decimal value)

3. Output for Vref = 1 V and input 10110:
   A. 0.4375 V
   B. 0.7500 V
   C. 0.6875 V
   D. 0.5000 V
   Answer: C. 22/32 = 0.6875 V. (Key point: Output)

4. The resolution (1 LSB) is:
   A. 62.5 mV
   B. 125 mV
   C. 3.125 mV
   D. 31.25 mV
   Answer: D. 1 V/32 = 31.25 mV. (Key point: Resolution)

## Related in Advanced Electronics

- [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
- [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
- [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×
- [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
- [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
- [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×

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