Homework #7

Section 2.6 page 180 in textbook

1. #30 part a Find the one’s complement representations, using bit strings of length six, of 22₁₀

2. #30 part c Find the one’s complement representations, using bit strings of length six, of -7₁₀

3. #36 part a Find the two’s complement representations, using bit strings of length six, of 22₁₀

4. #36 Part c Find the two’s complement representations, using bit strings of length six, of -7₁₀

The next 6 questions relate to the Boolean function described below by a Karnaugh map:

	cd
ab	\	00	01	11	10
	00	1			1
	01	1	x		1
	11	x		1
	10	1		1

5. find its simplest Product of Sums expression

F(a,b,c,d) = (c+d’)(a+d’)(a’+c’+d)

6. find its equivalent Sum of Products expression

F(a,b,c,d) = c’d’ +a’d’ + acd

7. Using truth tables, show that your answers to 5 and 6 produce the same function

8. Write the answer to #6 in disjunctive normal form

c’d’ = ac’d’ + a’c’d’ = abc’d’ + ab’c’d’ + a’b’c’d + a’bc’d …

9. Write the answer to #5 in conjunctive normal form

10. Using MMLogic (or any other circuit design program) - construct the circuit for either #5 or #6 (inputs should be switches, output should be a lamp). Bring a disk with your circuit on it to class (as well as a printout).