Question

For an 8-bit Digital to Analog Converter (DAC), the binary input 0000 0000 results in 0 V, and 1111 1111 results in 5 V. The output of the DAC for an input of 1011 0111 is ________ (in volts, rounded off to two decimal places).

Hint:

In a DAC, the output voltage can be calculated by multiplying the decimal equivalent of the binary input by the voltage step size. The voltage step is determined by the number of bits and the voltage range (in this case, 0 V to 5 V).

Answer 1

An 8-bit DAC can represent \( 2^8 = 256 \) distinct values, ranging from 0 to 255. The given inputs correspond to the following:
Binary input \( 0000 0000 \) corresponds to 0 V.
Binary input \( 1111 1111 \) corresponds to 5 V.
Each step between these values represents a voltage change of: \[ {Voltage step} = \frac{5 { V} - 0 { V}}{255} = \frac{5}{255} \approx 0.0196 { V}. \] The binary input \( 1011 0111 \) is equivalent to the decimal value: \[ 1011 0111_2 = 1 \times 2^7 + 0 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 183_{10}. \] The voltage corresponding to the input value 183 is: \[ {Output voltage} = 183 \times 0.0196 \approx 3.58 { V}. \] Thus, the output voltage for the input \( 1011 0111 \) is approximately \( 3.58 \) V.