The excess-3 binary code is obtained from the usual base 2 numbers (binary code by adding 3₁₀= 0011₂ to each of the codes. For example, 0011_excess-3= 0₁₀, 0100_excess-3 = 1₁₀ and 1010_excess-3= 7₁₀.

Some 4-bit numbers in excess-3 are invalid in that they do not represent a decimal digit, such as 0000. Some 4-bit numbers in excess-3 represent a value greater than 9₁₀, such as 1111_excess-3 and can be considered invalid when the output is only one decimal digit.

In this question we will design an excess-3 error detector. The circuit should detect whether a 4-bit input number has an invalid input in the sense that it does not represent a decimal digit. An output signal Error should be 1 if the input is invalid and it should be 0 if the input represents a decimal digit.

(a)Show the truth table for the excess-3 error detector.

(b)Give a Boolean formula for the output error signal in sum of products form.

(c)Simplify the expression from part (b).

(d)Draw the logic/circuit diagram for your simplified expression.