← Dashboard 1.4.3 Boolean Algebra A-Level Computer Science
Learning Objectives Notes Flashcards Quiz Exam Questions

Fill in the blanks with the correct words. Click "Check Answer" to see if you're right!

Term: Define Boolean logic.

Definition:

logic is the set of of logic based on binary values, where values are either (1) or (0), and is used to make logical decisions in computer science and electronics.
No attempts
Term: What is the difference between Boolean logic and Boolean algebra?

Definition:

refers to the of logic based on binary values, while Boolean algebra is a mathematical system used to manipulate Boolean values.
No attempts
Term: In Boolean logic, the value _________ represents TRUE, and _________ represents FALSE.

Definition:

In logic, the 1 represents TRUE, and 0 represents FALSE.
No attempts
Term: True or False? In Boolean expressions, OR operations are evaluated before AND operations unless parentheses are used.

Definition:

False. In expressions, AND are evaluated before OR unless parentheses change the order.
No attempts
Term: Define Exclusive Disjunction (XOR) in Boolean logic.

Definition:

(XOR) is a operator that returns TRUE if and only if the inputs are different, and FALSE if they are the same.
No attempts
Term: The _________ gate inverts its input, so NOT TRUE = FALSE and NOT FALSE = TRUE.

Definition:

The NOT its input, so NOT = FALSE and NOT FALSE = TRUE.
No attempts
Term: Define truth table.

Definition:

A table is a tool used in logic and to visualise the results of expressions. It lists all possible inputs and the associated outputs for a given Boolean expression.
No attempts
Term: What does each row in a truth table represent?

Definition:

Each in a represents a unique combination of inputs and the associated output for a Boolean expression.
No attempts
Term: A truth table shows all possible _________ and their associated _________ for a given Boolean expression.

Definition:

A all possible inputs and their associated outputs for a given Boolean expression.
No attempts
Term: True or False? Truth tables can be used to check the correctness of logic circuits.

Definition:

. allow you to systematically check all possible inputs and outputs of a logic circuit to verify its correctness.
No attempts
Term: In a truth table for an AND gate, the output is _________ only when both inputs are 1.

Definition:

In a for an AND gate, the is 1 only when both inputs are 1.
No attempts
Term: Define exclusive disjunction (XOR).

Definition:

An (XOR) is a operation that returns true only when exactly one of the inputs is true. If both inputs are the same, it returns false.
No attempts
Term: Define Karnaugh map.

Definition:

A map is a visual tool used to algebra expressions, making it easier to identify and eliminate redundant terms when designing digital circuits.
No attempts
Term: What is the main purpose of using a Karnaugh map in digital logic design?

Definition:

The of using a map is to simplify Boolean algebra expressions, making it easier to create efficient digital circuits.
No attempts
Term: In a Karnaugh map, _________ are grouped together in rectangles, and each group must contain a number of cells that is a power of 2.

Definition:

In a map, 1s are in rectangles, and each group must contain a number of cells that is a power of 2.
No attempts
Term: True or False? Each group in a Karnaugh map can only include cells that are adjacent horizontally or vertically, not diagonally.

Definition:

. Groups in a must include only cells that are adjacent horizontally or vertically; diagonal grouping is not allowed.
No attempts
Term: Define Karnaugh Map (KMap).

Definition:

A ( ) is a diagram used to simplify Boolean expressions with 2 or more inputs by visually grouping terms.
No attempts
Term: What is the first step in creating a Karnaugh Map for two variables?

Definition:

The is to add each , starting with A at the top and B down the side, and to add each possible state for both variables.
No attempts
Term: To fill a KMap for the expression A V B, you find all cells where either _________ or _________ is 1 and place a 1 in those cells.

Definition:

To a for the A V B, you find all cells where either A or B is 1 and place a 1 in those cells.
No attempts
Term: True or False? After filling all cells for each variable in a KMap, the map is complete for the given Boolean expression.

Definition:

. Once you have added 1s for all where each in the Boolean expression is 1, the KMap represents the expression fully.
No attempts
Term: Define Karnaugh map (for minimization).

Definition:

A is a diagram used to simplify expressions by organizing truth values into a grid to easily identify groups for minimization.
No attempts
Term: What is the main goal when grouping 1s in a Karnaugh map?

Definition:

The is to make the largest possible rectangular groups containing 1s, so the expression can be simplified as much as possible.
No attempts
Term: In a Karnaugh map, groups can only be formed in shapes that are _________ and must contain _________ 1s (e.g. 1, 2, 4, or 8).

Definition:

In a map, can only be in shapes that are rectangular and must contain powers of two 1s (e.g. 1, 2, 4, or 8).
No attempts
Term: True or False? Groups in a Karnaugh map may overlap and can wrap around the edges of the map.

Definition:

. can overlap and wrap around the edges of a map to ensure the largest possible simplification of the Boolean expression.
No attempts
Term: Define De Morgan's Law.

Definition:

De Law is a for that include a negation of a conjunction or disjunction. It allows you to invert variables and change AND to OR (or vice versa) when negating logical expressions.
No attempts
Term: True or False? NOT(A AND B) is logically equivalent to (NOT A) OR (NOT B).

Definition:

. to De Morgan's Law, the negation of a conjunction (AND) is to the disjunction (OR) of the negated terms: AND B) = (NOT A) OR (NOT B).
No attempts
Term: To apply De Morgan's Law, change _________ to OR (or vice versa) and negate each term.

Definition:

To De Law, AND to OR (or vice versa) and negate each term.
No attempts
Term: Why is De Morgan's Law useful in building microprocessors?

Definition:

De is because it allows logical expressions to be simplified so that only NAND or NOR gates are needed, which makes microprocessor design easier and more efficient.
No attempts
Term: Define associative law.

Definition:

The law states that how are in an with only AND or only OR does not affect the outcome, e.g., (A AND B) AND C = A AND (B AND C) = A AND B AND C.
No attempts
Term: Define distributive law.

Definition:

The law how AND and OR in logic, you to distribute one over the other: A AND (B OR C) = (A AND B) OR (A AND C).
No attempts
Term: True or False? A OR (B AND C) is equivalent to (A OR B) AND (A OR C).

Definition:

. to the law, A OR (B AND C) is the same as (A OR B) AND (A OR C).
No attempts
Term: The associative law allows us to remove _________ and regroup variables in expressions, so (A OR B) OR C is the same as A OR (B OR C).

Definition:

The us to remove brackets and regroup variables in expressions, so (A OR B) OR C is the same as A OR (B OR C).
No attempts
Term: Define commutative law.

Definition:

The law states that the order of the does not change the truth value of the , such as A AND B being the same as B AND A.
No attempts
Term: True or False? A OR B is different from B OR A in Boolean logic.

Definition:

. to the law, A OR B is the same as B OR A.
No attempts
Term: The commutative law states that _________ of variables does not change the truth value of the expression.

Definition:

The that the order of variables does not change the truth value of the expression.
No attempts
Term: Define double negation law.

Definition:

The law states that applying NOT twice to a variable returns the original variable, so )) = A.
No attempts
Term: According to the double negation law, NOT(NOT(A)) = _________.

Definition:

to the negation law, NOT(NOT(A)) = A.
No attempts
Term: How does the commutative law help when simplifying Boolean expressions, such as in the worked example (A v B) ^ (A v C)?

Definition:

The allows you to variables in expressions (e.g., changing B AND A to A AND B), which helps to group like terms and apply further simplifications when working through expressions like (A v B) ^ (A v C).
No attempts
Term: Define D type flip flop.

Definition:

A D flop is a circuit component used to store a single bit of data and is triggered by the rising edge of the clock pulse.
No attempts
Term: What are the two outputs of a D type flip flop called?

Definition:

The are Q and NOT(Q).
No attempts
Term: A D type flip flop contains _________ stable states, making it a _________ circuit.

Definition:

A D flop contains two stable states, making it a bistable circuit.
No attempts
Term: What happens to the output Q of a D type flip flop on the rising edge of the clock pulse if D is high?

Definition:

If D is high on the of the pulse, Q goes high and NOT(Q) goes low.
No attempts
Term: True or False? A D type flip flop can change its output Q at any time when D changes.

Definition:

False. A D only changes its output Q on the rising edge of the clock pulse, not whenever D changes.
No attempts
Term: The _________ input of a D type flip flop provides the data to be stored, while the _________ input controls when the state may change.

Definition:

The D of a D flop provides the data to be stored, while the CLK input controls when the state may change.
No attempts
Term: Name one common use of D type flip flops in digital circuits.

Definition:

D flops are commonly used in shift registers, counters, and memory units.
No attempts
Term: D type flip flops are often referred to as _________ edge triggered devices.

Definition:

D flops are often referred to as positive edge triggered edge triggered devices.
No attempts
Term: Define half adder.

Definition:

A adder is a basic digital circuit used to add two single-bit binary numbers, producing a Sum (S) and a out ( ) output.
No attempts
Term: What are the inputs and outputs of a half adder circuit?

Definition:

A adder circuit has two , labelled A and B, and two : Sum (S) and Carry out (Cout).
No attempts
Term: In a half adder, the _________ output is produced using an _________ gate, and the _________ output is produced using an XOR gate.

Definition:

In a adder, the Carry out (Cout) is using an AND gate, and the Sum (S) output is produced using an XOR gate.
No attempts
Term: True or False? The output of a half adder's Sum is created using an AND gate.

Definition:

False. The in a adder is produced using an XOR gate, not an AND gate.
No attempts
Term: When both inputs A and B of a half adder are 1, the binary sum is _________, meaning Carry out is _________ and Sum is _________.

Definition:

When both A and B of a are 1, the binary sum is 10, meaning Carry out is 1 and Sum is 0.
No attempts
Term: Which logic gates are used to build a half adder circuit?

Definition:

A circuit uses an XOR gate for the Sum output and an AND gate for the out output.
No attempts
Term: Define full adder.

Definition:

A adder is a logic that adds three binary inputs (A, B, and Cin) and produces two outputs: sum (S) and carry ( ).
No attempts
Term: A full adder circuit has _________ inputs (A, B, Cin) and _________ outputs (S, Cout).

Definition:

A circuit has three inputs (A, B, Cin) and two outputs (S, Cout).
No attempts
Term: True or False? The sum output of a full adder is the result of XOR-ing all three inputs: A, B, and Cin.

Definition:

. The (S) of a full adder is calculated by XOR-ing A, B, and Cin. This means S = A ⊕ B ⊕ Cin.
No attempts
Term: How can you use full adders to add two 4-bit binary numbers?

Definition:

You can 4-bit binary numbers by connecting four in series, with the carry output (Cout) of each adder connected to the carry input (Cin) of the next.
No attempts