EEE 120 CERTIFICATION PAPER 2026 FULL
SOLUTION 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
● How to represent a number in different bases (Base- 2, base- 8, base-
10, base- 16) Answer: Binary Base-2: 00, 01, 10, 11, 100, 101, 110, 111
Octal Base-8: 0, 1, 2, 3, 4, 5, 6, 7, 10
Decimal Base-10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Hexadecimal Base-16: 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B,C,D,E,F
SOLUTION 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
● How to represent a number in different bases (Base- 2, base- 8, base-
10, base- 16) Answer: Binary Base-2: 00, 01, 10, 11, 100, 101, 110, 111
Octal Base-8: 0, 1, 2, 3, 4, 5, 6, 7, 10
Decimal Base-10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Hexadecimal Base-16: 1, 2, 3, 4, 5, 6, 7, 8, 9, A,B,C,D,E,F
