CSUC101_Unit2_EVEN

If P, Q, R are Boolean variables, then (P + Q') (P.Q' + P.R) (P'R' + Q') Simplifies to

• PQ'

• PR'

• PQ'+R

• PR+Q

Given f1,f3 and f in canonical sum of products from (in decimal) for the circuit. F1 = Σm (4,5,6,7,8) F3 = Σm (1, 6, 15) F = Σm (1, 6, 8, 15). Then f2 is

• Σm (4, 6)

• Σm (4, 8)

• Σm (6, 8)

• Σm (4, 6, 8)

Given f(w, x, y, z) = Σm(0, 1, 2, 3, 7, 8, 10) + Σd(5, 6, 11, 15), where d represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w, x, y, z)?

• 𝑓 =(𝑤' +𝑧')(𝑥'+𝑧)

• 𝑓 =(𝑤'+𝑧)(𝑥 +𝑧)

• 𝑓 =(𝑤+𝑧)(𝑥' +𝑧)

• 𝑓 =(𝑤+𝑧')(𝑥' +𝑧)

In the Karnaugh map shown below, X denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

• b'd'+a'd'

• a'b'+b'd'+a'bd'

• b'd'+a'bd'

• a'b'+b'd'+a'd'

Which one of the following is NOT a valid identity?

• 
• 
• 
• 

Given the function F = P’ + QR, where F is a function in three Boolean variables P,Q and R and P’ = !P, consider the following statements. (S1) F = Σm(4, 5, 6) (S2) F = Σm(0,1,2,3,7) (S3) F = Σm(4, 5, 6) (S4) F = Σm(0,1,2,3,7) Which of the following is true?

• (S1) – False, (S2) – True, (S3) – True, (S4) -False

• (S1) – True, (S2) – False, (S3) – False, (S4) -True

• (S1) – False, (S2) – False, (S3) – True, (S4) -True

• (S1) – True, (S2) – True, (S3) – False, (S4) -False

A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those. Which of the following sets of connectives is NOT functionally complete?

• NAND

• implication, negation

• OR, negation

• EX-NOR