#20 Boolean Algebra

1. A leisure centre has some rules about who can join based on their criminal record and whether they live locally. Let R denote that a person is resident in an area. Let C denote that a person has a serious criminal conviction. Let P denote whether a person is permitted to become a member of the local leisure centre. Which of the following expressions represents the following statement: 'To be a member, individuals must reside in the area and must not have any serious criminal convictions'?

• A. P=R+C
• B. PR.C
• C. P = R. Not(C)
• D. P = Not(R.C)

2. A bank will only lend money to a house buyer (as a mortgage) if they pass the affordability checks, have a good credit history and have a 10% deposit. Let A denote that a person can afford the repayments on the mortgage based on their current income. Let C denote that a person has a good credit history. Let D denote that a person has saved a 10% deposit. Let L denote whether a bank is willing to offer a loan/mortgage for buying the house. Which of the following expressions correctly describes the scenario?

• A. L= ACD
• B. L=A+C+D
• C. L= A.C + D
• D. L = A + C.D

3. Let A, B, C and D be Boolean variables. Use the associativity law to rewrite the Boolean expression: (A+B)+(C+D)

• A. A.B + C.D
• B. Not(A.B) +Not(C.D)
• C. A+(B+C)+D
• D. A.B.C.D

4. Study the logic circuit diagram below. Which of these is the equivalent logical expression?

• A. Q = not(A) and (A xor B)
• B. Q = not(A xor B) and A
• C. Q = A and B and not(A xor B)
• D. Q= A or B and not(A)

5. A logic expression uses four inputs: A, B, C and D. A truth table is being constructed. How many rows does it need?

• A. 32
• B. 8
• C. 4
• D. 16

6. Reading downwards, what are the missing bits in the truth table shown?

• A. 01101
• B. 11011
• C. 01010
• D. 00110

7. Study the truth table and the logic diagrams below. Which of the logic circuit diagrams corresponds to the truth table?

• A. Option 1
• B. Option 2
• C. Option 3
• D. Option 4

8. Simplify the expression: (A and not(B)) and (A or not(C))

• A. A and not(B) or not(C)
• B. A and not(B)
• C. B and not(C or A)
• D. Cand (A or not(B))

9. Which of these is a false statement about Karnaugh maps?

• A. They allow the user to apply Boolean algebra laws such as associativity to simplify expressions in Boolean algebra
• B. Gray code must be used to set up the row and column headings
• C. They are a tool for simplifying Boolean expressions
• D. They can work with two, three and four inputs
• B. Enqueue(owl), dequeue(), dequeue()

10. Study the Karnaugh map below. Which of these is the most simplified Boolean expression that can be derived from it?

• A. not(C).D+ not(A).not(B).not(C) + A.not(B).C + not(B).C.not(D)
• B. not(A).not(B) + A.not(B) + not(C).D
• C. not(A).not(B).not(C) + A.not(B).C+ not(C).D
• D. A.not(B).not(C) + not(A).not(B).C + not(C).not(D)