Question: (II) Consider a rather coarse 4-bit analog-to-digital conversion where the maximum voltage is 5.0 V. (a) What voltage does 1011 represent? (b) What is the 4-bit representation for 2.0 V?

A signal voltage varies in time and they are used in electronic devices.Signal voltage can be analog as well as digital. In digital signals, a binary number system is used to represent a numerical value.

A four-digit binary number can represent the lowest decimal number 0 and the highest decimal number 15.

So, 5.0 V is equivalent to 15.

Then, each binary number represents\(\frac{{5.0\;{\rm{V}}}}{{15}} = \frac{1}{3}\;{\rm{V}}\).

Now you can find the decimal equivalent of 1011 as follows,

\(\mathop 1\limits^3 \mathop 0\limits^2 \mathop 1\limits^1 \mathop 1\limits^0 \)

Then the binary number equivalent is,

\(\begin{aligned}{c}{2^3} + {2^1} + {2^0} &= 8 + 2 + 1\\ &= 11\end{aligned}\)

So, the decimal equivalent of 1011 is 11.

Then, the equivalent voltage of binary digit 1011 is,

\(11 \times \frac{1}{3}\;{\rm{V}} = 3.67\;{\rm{V}}\)

Thus, 1101 represents a voltage of 3.67 V.

Let N be equivalent of the voltage 2.0 V.

Now you get,

\(\begin{aligned}{c}N \times \frac{1}{3}\;{\rm{V}} &= 2.0\;{\rm{V}}\\N &= 6\end{aligned}\)

The binary equivalent of 6 is 0110.

Thus, the binary representation of 2.0 V is 0110.