Logic functions and Minimization

Question 11

Given f₁, f₃ and f in canonical sum of products form (in decimal) for the circuit

A) m(4, 6)

B) m(4, 8)

C) m(6, 8)

D) m(4, 6, 8)

• A
• B
• C
• D

Question 12

If P, Q, R are Boolean variables, then (P + Q\')(PQ\' + PR)(P\'R\' + Q\') simplifies

• PQ\'
• PR\'
• PQ\' + R
• PR\'\' + Q

Question 13

Consider the following Boolean function of four variables: f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) The function is:

• independent of one variables.
• independent of two variables.
• independent of three variables.
• dependent on all the variables.

Question 14

Let f(w, x, y, z) = ∑(0, 4, 5, 7, 8, 9, 13, 15). Which of the following expressions are NOT equivalent to f?

• x\'y\'z\' + w\'xy\' + wy\'z + xz
• w\'y\'z\' + wx\'y\' + xz
• w\'y\'z\' + wx\'y\' + xyz + xy\'z
• x\'y\'z\' + wx\'y\' + w\'y

Question 15

Define the connective * for the Boolean variables X and Y as: X * Y = XY + X\' Y\'. Let Z = X * Y.

Consider the following expressions P, Q and R.
P: X = Y⋆Z 
Q: Y = X⋆Z 
R: X⋆Y⋆Z=1

Which of the following is TRUE?

• Only P and Q are valid
• Only Q and R are valid.
• Only P and R are valid.
• All P, Q, R are valid.

Question 16

Consider the following Boolean expression for F:

F(P, Q, R, S) = PQ + P\'QR + P\'QR\'S

The minimal sum-of-products form of F is

• PQ + QR + QS
• P + Q + R + S
• P\' + Q\' + R\' + S\'
• P\'R + P\'R\'S + P

Question 17

Consider the following minterm expression for F : F(P,Q,R,S) = ∑ (0, 2, 5, 7, 8, 10, 13, 15) The minterms 2, 7, 8 and 13 are \'do not care\' terms. The minimal sum-of-products form for F is :

• QS\' + Q\'S

• Q\'S\' + QS

• Q\'R\'S\' + Q\'RS\' + QR\'S + QRS

• P\'Q\'S\' + P\'QS + PQS + PQ\'S\'

Question 18

Let X denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:

F(P, Q) = ( ( 1 X P) X (P X Q) ) X ( (P X Q) X (Q X 0) ) 

The equivalent expression for F is

• P + Q
• (P + Q)\'
• P X Q
• (P X Q)\'

Question 19

Consider a Boolean function f (w, x, y, z). suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = (w1, x1, y1, z1) and i2 = (w2, x2, y2, z2) we would like the function to remain true as the input changes from i1 to i2 (i1 and i2 differ in exactly one bit position), without becoming false momentarily. Let f (w, x, y, z) = ∑(5,7,11,12,13,15). Which of the following cube covers of f will ensure that the required property is satisfied?

• w\'xz, wxy\', xy\'z, xyz,wyz

• wxy,w\'xz,wyz

• wx(yz)\', xz, wx\'yz

• wzy, wyz, wxz, w\'xz, xy\'z, xyz

Question 20

Consider numbers represented in 4-bit gray code. Let h3h2h1h0 be the gray code representation of a number n and let g3g2g1g0 be the gray code of (n + 1) (modulo 16) value of the number. Which one of the following functions is correct? A: [Tex]g_{0}(h_{3},h_{2},h_{1},h_{0})=\\sum (1,2,3,6,10,13,14,15)[/Tex] B: [Tex]g_{1}(h_{3},h_{2},h_{1},h_{0})=\\sum (4,9,10,11,12,13,14,15)[/Tex] C: [Tex]g_{2}(h_{3},h_{2},h_{1},h_{0})=\\sum (2,4,5,6,7,12,13,15)[/Tex] D: [Tex]g_{3}(h_{3},h_{2},h_{1},h_{0})=\\sum (0,1,6,7,10,11,12,13)[/Tex]

• A

• B

• C

• D