COMPLETE TEST BANK PAPER 2026
EXTENSIVE EXAM QUESTIONS TOGETHER
WITH FULLY EXPLAINED CORRECT
ANSWERS GRADED A+
⩥ AND A*B. Answer: ~(A AND B) = ~A OR ~B
⩥ OR A+B. Answer: ~(A OR B) = ~A AND ~B
⩥ NOT ~A. Answer: ~A
⩥ NAND ~(A*B). Answer: ~(A AND B) = ~A OR ~B
⩥ NOR ~(A+B). Answer: ~A AND ~B
⩥ XOR A ⨁ B. Answer: ~(A ⨁ B)
⩥ Boolean Functions. Answer: A function that returns either true or false
,⩥ How to represent a Boolean function in a truth table:. Answer: Step 1:
Label your variables on the top row, and fill in with binary count going
down
Step 2: Identify your equation and simplify it (use DeMorgan's rule if
necessary, ie, (ab)' = a' + b' )
Step 3: Find which terms output 1 or 0 (if 1 combination is 1, then the
entire row comes out to 1 if you are using OR's)
⩥ How to represent a Boolean function in shorthand/algebraic form,
including SOP and POS forms. Answer: Distributive rule: (a+b)(a+c) =
a+bc
(x'+z')(x'+y+z) = (x'+z')(y+z)
Special case: (a+b)(a+b') = a+bb' = a
Associative rule: ((x'+z')+y')((x'+z')+y) = (x'+z')
POS: For odd number of terms w/same number of values: replicate
⩥ Minimize a Boolean function via Boolean algebra and also using K-
maps. Answer: a'b'c' + a'b'c + abc + ab'c
a'b'(c' + c) + ac(b' + b)
a'b' + ac
See where the function becomes a 1 from last equation
K-map (stars represent number of times circled)
c
a b | 01
, ---------
00 | 1*1*
01 | 00
11 | 01*
10 | 01*
a'b' + ac
⩥ How to implement an arbitrary Boolean function using
AND/OR/NOT gates, using only NAND gates, and using only NOR
gates. Answer: Types of gates you can recreate using NAND:
NOT - One NAND gate
AND - One NAND gate in front of the other
OR - Two NAND gates side by side feeding into one NAND
Types of gates you can recreate using NOR:
NOT - One NOR gate
OR - One NOR gate in front of the other
AND - Two NOR gates side by side feeding into one NOR
Note* You can cancel out two NOTs/NANDs/NORs