Quiz: Boolean Algebra, Functions and Implementation

A city traffic controller uses a 3-input logic set: P (pedestrian request), V (vehicle sensor), N (night mode). The controller must give WALK signal when a pedestrian has requested and it is safe: either (a) vehicle sensor is OFF, or (b) it is night mode (which uses reduced vehicle flow). The WALK output should not activate if there is an active emergency override E (active = 1) that forces STOP regardless. Boolean expression for WALK (ignore E) that is true when P=1 and (V=0 or N=1) is:

• A. P(V̅ + N)

• B. PV' + PN'

• C. P(V + N)

• D. P(V + N)

A city traffic controller uses a 3-input logic set: P (pedestrian request), V (vehicle sensor), N (night mode). The controller must give WALK signal when a pedestrian has requested and it is safe: either (a) vehicle sensor is OFF, or (b) it is night mode (which uses reduced vehicle flow). The WALK output should not activate if there is an active emergency override E (active = 1) that forces STOP regardless. If emergency override E must force WALK = 0 (i.e., inhibit walk when E=1), the combined expression is:

• A. P(V̅ + N) + E'

• B. P(V̅ + N) . E̅

• C. P(V̅ + N) + E

• D. P(V̅ + N) ⊕ E

Which Boolean theorem justifies factoring P(V̅ + N) into sum-of-products for K-map minimization?

• A. De Morgan’s theorem

• B. Distributive law

• C. Consensus theorem

• D. Absorption law

Convert F=PV̅+PN to a minimal SOP using algebraic simplification — what is minimal?

• P(V̅ + N) (already minimal)

• P

• P(V̅N)

• V̅ + N

A city traffic controller uses a 3-input logic set: P (pedestrian request), V (vehicle sensor), N (night mode). The controller must give WALK signal when a pedestrian has requested and it is safe: either (a) vehicle sensor is OFF, or (b) it is night mode (which uses reduced vehicle flow). The WALK output should not activate if there is an active emergency override E (active = 1) that forces STOP regardless. Suppose you must implement F=PV̅+PN using only NAND gates. The minimal number of two-input NAND gates required to realize the function (without using multi-input NANDs) is:

If P=1, V=1, N=0, E=0 what is WALK?

• 1

• 0

• Undefined

• Oscillating

An elevator has card reader (C), overload sensor (O), and floor selector valid (F). Door unlock U only when C=1 AND F=1 AND O=0.

• CF'O

• C + F + O'

• (C + F)O'

• C(F + O')

An elevator has card reader (C), overload sensor (O), and floor selector valid (F). Door unlock U only when C=1 AND F=1 AND O=0. Using De Morgan, express U̅:

• C̅ + F̅ + O

• C̅ · F̅ · O

• C'F'O'

• (CF) + O̅

An elevator has card reader (C), overload sensor (O), and floor selector valid (F). Door unlock U only when C=1 AND F=1 AND O=0. 9. The designer wants a fail-safe using NAND only; tying inputs appropriately, a NAND that receives C and F and O' (inverter on O) yields U directly. True or false?

• True — single NAND with O inverted works

• False — NAND produces complement, extra inversion needed

• True only if C and F are tied together first

• False unless using three-input NAND

An elevator has card reader (C), overload sensor (O), and floor selector valid (F). Door unlock U only when C=1 AND F=1 AND O=0. If the minimization yields U=CF O̅, the canonical minterm form (three variables) is:

• Σ(7) (where minterm numbers assume order C,F,O)

• Σ(3, 5)

• Σ(4, 5, 6, 7)

• Σ(2, 3, 6, 7)