OCR A Level CS 1.4.3 Boolean Algebra
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20 Terms
What is Boolean algebra?
A form of algebra that deals with true (1) or false (0) values.
What are the three basic Boolean operations?
AND (∧), OR (∨), NOT (¬).
What is the function of the AND operator?
Returns 1 only if both inputs are 1; otherwise, it returns 0.
What is the function of the OR operator?
Returns 1 if at least one input is 1; otherwise, it returns 0.
What is the function of the NOT operator?
Inverts the input (0 → 1, 1 → 0).
What is a truth table?
A table showing all possible input combinations and their corresponding output.
A | B | A AND B (∧) | A OR B (∨) | A XOR B (⊕) | NOT A (¬A) |
|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 0 |
What are De Morgan’s Laws?
¬(A ∧ B) = ¬A ∨ ¬B
¬(A ∨ B) = ¬A ∧ ¬B
What is the commutative law?
Order of inputs doesn’t matter:
A ∧ B = B ∧ A
A ∨ B = B ∨ A
What is the associative law?
Grouping of inputs doesn’t matter:
(A ∧ B) ∧ C = A ∧ (B ∧ C)
(A ∨ B) ∨ C = A ∨ (B ∨ C)
What is the distributive law?
A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)
What is double negation?
¬(¬A) = A (negating twice cancels out).
What is a Karnaugh map?
A method to simplify Boolean expressions by grouping 1s in a truth table.
What are the rules for grouping 1s in a Karnaugh map?
Groups must be powers of 2 (1, 2, 4, 8...).
Groups should be as large as possible.
Wraparound is allowed (edges connect).
Overlapping groups are allowed.
What is the simplified expression from the Karnaugh map?
The sum of the grouped terms.
What are logic circuits?
Physical representations of Boolean expressions using logic gates.
What is a D-type flip-flop?
A circuit that stores a single bit and updates its value on a clock pulse.
What is the purpose of a clock signal in a flip-flop?
Ensures that changes happen at precise timing intervals.
What is a half adder?
A circuit that adds two single-bit inputs and produces:
Sum bit (S) = A XOR B
Carry bit (C) = A AND B
What is a full adder?
A circuit that adds three inputs (A, B, Cin) and produces:
Sum = A ⊕ B ⊕ Cin
Carry out = (A ∧ B) ∨ (Cin ∧ (A ⊕ B))
Why are full adders used instead of half adders?
Full adders allow multi-bit binary addition by handling carry bits.
Note 
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