1.4.3 Boolean Algebra
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What does the AND gate do and what is its symbol?
It outputs 1 if both input values are 1. The symbol is: ∧
What does the OR gate do and what is its symbol?
It outputs 1 if at least 1 input’s value is 1. The symbol is: ∨
What does the NOT gate do and what is its symbol?
It reverses the value of an input, from 0 to 1 or vice versa. The symbol is: ¬
What does the XOR gate do and what is its symbol?
It outputs 1 only if one input is 1, but not if both inputs are 1. The symbol is: ⊻
What is the purpose of a truth table?
It’s used to showcase all possible input combinations for a logic circuit or Boolean expression, alongside the resulting output for each combination.
What is the purpose of a Karnaugh map?
It’s a visual method used to simplify Boolean expressions and make logic circuits more efficient.
What is De Morgan’s Law for simplifying Boolean expressions?
It states that ¬(A AND B) = (¬A OR ¬B). And states that ¬(A OR B) = (¬A AND ¬B). This shows how to distribute negation across AND and OR operations.
What is the Distributive Law for simplifying Boolean expressions?
It states that A AND (B OR C) = (A AND B) OR (A AND C). This allows expressions to be expanded or factored.
What is the Associative Law for simplifying Boolean Expressions?
It states that (A AND B) AND C = A AND (B AND C). It also states that (A OR B) OR C = A OR (B OR C). This shows that the grouping of terms doesn’t affect the result.
What is the Commutative Law for simplifying Boolean Expressions?
It states that A AND B = B AND A and A OR B = B OR A. This shows that the order of terms doesn’t matter.
What is the Double Negation rule used for simplifying Boolean expressions?
It states that ¬¬A = A. This shows that 2 NOTS cancel each other out.
What is the purpose of a logic gate diagram?
Logic gate diagrams are visual representations of Boolean expressions or digital circuits, showing how data flows through logic gates to produce an output.
Do you know the AND Gate?
Do you know the OR Gate?
Do you know the NOT Gate?
Do you know the XOR Gate?
Describe the inputs and outputs used by a D-type flip-flop circuit, explaining how the inputs are used to control the outputs.
The inputs include Data input (often labelled D) and Clock input. It has 2 outputs: Q output and the inverse of Q (NOT Q). When the clock input goes high Q changes to D.
What is the purpose of a D-type flip-flop circuit?
To delay or store a value of 1 bit when a signal is given.
What are D-type flip-flops useful for?
They’re useful for memory storage and transfer and data synchronisation.
Where are D-type flip-flops used?
They’re used in memory circuits in CPU registers and RAM.
Do you know what a half adder looks like?
Do you know what a full adder looks like?
Describe a half adder
A logic circuit with 2 inputs (A and B) that are added to produce 2 outputs, S (sum), the result of A XOR B, and C (carry) the result of A AND B. They can only add 2 bits and can’t handle an input carry from a. previous addition.
Describe the structure of a full adder and their main use
A full adder is an extension of a half adder with 3 inputs: A, B, AND Cin (a carry-in from the previous calculation). It produces 2 outputs: S (sum, which is (A XOR B XOR Cin)) and C out (carry out, which is (A AND B) OR (B AND Cin) OR (A AND Cin)). Full adders can be linked together to perform multi-bit binary addition in arithmetic circuits.