Homework 1

Due: Friday, September 15, 2017, 9:00 am (start of the class)

- What is the 4-bit 2's complement representation of -5?
- Using 4-bit binary numbers, add 3 and -6 (in binary). Show all of the carries into each column. Show that the answer is correct.
- Given the truth table below, fill out a 4-variable Karnaugh map.
A B C D F 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0

CD 00 01 11 10 ----------------------------- AB 00 01 11 10

- Given the Karnaugh map from question #3, extract the optimal Boolean expression in Sum-of-Products form.
- Given the Boolean expression in #4, show the corresponding circuit diagram.

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