Question

Suppose you have an electronic signal with possible voltage values "V" between 0 and 16 volts, and you want to represent these values with a 4 bit number ranging from smallest (0000, for voltages in the range 0 volts <= V < 1 volt) to largest (1111, for 15 volts <= V < 16 volts). What is the bit pattern for the voltage value V= 9.5 volts?

Answer 1

Lets first convert 9 to bit pattern.

Dividing 9 continuosly by 2 until the quotient is 0, the remainders we get are 1, 0, 0 and 1 respectively.

So, bit pattern for 9 is in the reverse order of remainders we got, which is 1001.

Now, we need to convert 0.5 to bit pattern.

Multiplying 0.5 by 2, the whole number we get is the first binary digit after point, which is 1 here. Since the fractional part of the resultant is no more, the bit pattern for 0.5 is 1.

So, bit pattern for 9.5 is 1001.1