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

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.

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

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

 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).

✓ Answer checked by Claude Sonnet 5.5

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