The circuit below converts a positive, unsigned binary

Chapter 16, Problem 16.32

(choose chapter or problem)

The circuit below converts a positive, unsigned binary number into a BCD decimal number. The binary number is entered bit serially with the most significant bit first. As each input bit is entered, the BCD number in the registers is multiplied by 2 and the input bit added to it.

(a) Show the contents of the registers after each input bit for the binary number 110110111.

(b) What is the largest binary number that this circuit can correctly convert to BCD?

(c) Derive the minimum sum-of-product equations for the outputs of the BCD multiply by 2 circuit. Let \(x_{3}, x_{2}, x_{1}, x_{0}\) be the inputs and \(y_{3}, y_{2}, y_{1}, y_{0}\) be the outputs.