a 6-bit r-2r ladder da converter has a reference

Question

A 6-bit R-2R ladder D/A converter has a reference voltage of 6.5V. It meets standard linearity.Find
(i) The Resolution in Percent.
(ii) The output voltage for the word 011100.

Ans. Given Number of Bits (n) = 6
Reference Voltage (VR) = 6.5 V

So for R-2R Ladder D/A Converter,
(i)The Resolution in Percent is specified by

1/(2ⁿ-1) = 1/(2⁶-1) = 1/63 = 1.59%

(ii)The Output Voltage (VO) of six-bit R-2R Ladder D to A Converter for the word 011100 is specified by

V₀ = V_R/2ⁿ[a_n-12^n-1 + a_n-22^n-2 +...........+a₁2¹ + a₀2⁰]

V₀ = 6.5/2⁶[0.2 x 2^6-1 + 1 x 2^6-2 +1 x 2^6-1 + 0 x 2⁰]

V₀ = 6.5/2⁶[2⁴ + 2³ + 2²]

V₀ = 2.84 V.