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

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.

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.

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

Vo = V1 (b3/2 + b2/4 + b1/8 + b0/16),   V1 = 12 V
BitWeightOutput when only that bit is 1
b3 (MSB)1/212/2 = 6 V
b21/412/4 = 3 V
b11/812/8 = 1.5 V
b0 (LSB)1/1612/16 = 0.75 V

Resolution

The resolution is the output change for 1 LSB:

Resolution = V1 / 2⁴ = 12/16 = 0.75 V

Full scale output

Full scale output is the output for input 1111:

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

Output for input 1011

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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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