Chapter 3, Problem 56E

Explanation of Solution

Truth table:

The truth table will specifies the output condition for every input. The input values are all possible binary values of the input. Hence for “n” inputs, there are 2ⁿ possible combinations.

The task is to design a circuit that outputs an error BCD (Binary Code Decimal) format. In that format, every decimal digit 0 to 9, is coded as its binary equivalent.

The number of bits required to code the digits 0 to 9 that is 10 digits is Ceiling [log₂ (10)] = 4.

The first 10 binary codes that is 1010 to 1111, the error bit would be 1, since all these are invalid codes. This is because there are only 10 digits in the decimal system.

The below truth table will show the error function:

w

x

y

z

E