Question

1.

If you apply DeMorgan's theorem to the expression of Y above , which answer do you get? (a, b, c, or d)

Y=AB(C + BD) Options: a)Y=A+B+CBD b) =A+B+CB+D c) Y = AB + C(B + D))

2.

Which single two-input gate is equivalent to thecircuit of the figure above?
A. AND
B. OR
C. NAND
D. XNOR
E. XOR

3. A Code-Word generator is to be designed. It uses four binary inputs, ABCD, and one output f. The circuit works as follows: there are only six valid input code words. Each valid code word consists of four-bits words (ABCD) that always contain two “0” and two “1”, not necessarily in order, for instance ABCD = “0101” and ABCD = “1100” are valid code words. The output f will be “1” if the input is a valid code word that corresponds to an even number (using ABCD as binary number with A the most significant digit and D the less significant digit) and “0” if the input is a validinput code that corresponds to a odd number. For instance the code word “1010” will be interpreted as the number ten (an even number) and therefore the output f will be “1”. Observe that a combination such as ABCD ="1000" (contain three equal inputs) is not valid and it will never occur.

The expression for the function f is:
A. f = ?m(2,4,6,8,10,12,14,15)
B. f = ?m(8,9,10,11,12,13,14,15) + d(0,1,2,3,4,5,6,7)
C. f = ?m(6,10,12) + d(0,1,2,4,7,8, 11,13,14,15)
D. None of the above