(Design Problem) Extend the system of Exercise 1 with two or more outputs: F2 (that is 1 when the input is a multiple of 2) and F8 (that is 1 when the input is a multiple of 8).
(a) Repeat parts (a) through (c) of Exercise 1 for F2 and F8.
(b) Can you implement the function F4 in terms of F2? How?
(c) Can you implement the function F8 in terms of F4? How?
Exercise 1
(Design Problem) Consider a digital system that works as follows. It takes as input a number in the range of 010 to 1510 in binary and outputs a function, F4, that is 1 if the number is a multiple of 4.
(a) Develop the truth table for this function, with four binary inputs (00002 to 11112) and the output as indicated above.
(b) Write down the Boolean equations for the function F4.
(c) Characterize the complexity of this implementation by counting the number of AND, OR, and NOT gates of various input sizes needed to realize the output (e.g., so many 2- input ANDs, 3-input ANDs, etc.).
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