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5-bit R-2R DAC output for 10110

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.

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.

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

 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):

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

Calculation for input 10110, Vref = 1 V

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.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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