Digital Logic
What is Digital Logic?
A branch of algebra in which the variables take on only two values, typically 0 and 1, and the operations are logical operations such as AND, OR, and NOT.
Key formula / rule: AND Operation
Key points
- Understand the principles of Boolean algebra.
- Identify and describe the function of basic and universal logic gates.
- Construct truth tables for given Boolean expressions and logic gates.
- Simplify Boolean expressions using algebraic laws.
Common exam trap
Confusing AND and OR operations.
Definitions
- Term
Boolean Algebra
- Meaning
A branch of algebra in which the variables take on only two values, typically 0 and 1, and the operations are logical operations such as AND, OR, and NOT.
- Term
Logic Gate
- Meaning
An elementary building block of a digital circuit that performs a basic logical operation on one or more binary inputs and produces a single binary output.
- Term
Truth Table
- Meaning
A table that shows all possible input combinations for a logic circuit or Boolean expression and the corresponding output for each combination.
- Term
Universal Gate
- Meaning
A logic gate from which any other logic gate (AND, OR, NOT) can be constructed. NAND and NOR gates are universal gates.
Learning objectives
Understand the principles of Boolean algebra.
Identify and describe the function of basic and universal logic gates.
Construct truth tables for given Boolean expressions and logic gates.
Simplify Boolean expressions using algebraic laws.
Implement logic functions using combinations of logic gates.
Understand the concept of universal gates.
Formulae
- Name
AND Operation
- Note
Output is 1 only if both inputs A and B are 1.
- Expression
Y = A . B
- Name
OR Operation
- Note
Output is 1 if at least one input A or B is 1.
- Expression
Y = A + B
- Name
NOT Operation
- Note
Output is the inverse of the input A.
- Expression
Y = A'
- Name
NAND Operation
- Note
Output is the inverse of the AND operation.
- Expression
Y = (A . B)'
- Name
NOR Operation
- Note
Output is the inverse of the OR operation.
- Expression
Y = (A + B)'
- Name
XOR Operation
- Note
Output is 1 if the inputs A and B are different.
- Expression
Y = A ⊕ B = A'B + AB'
- Name
XNOR Operation
- Note
Output is 1 if the inputs A and B are the same.
- Expression
Y = A ⊙ B = A'B' + AB
- Name
De Morgan's Law 1
- Note
The complement of a sum is the product of the complements.
- Expression
(A + B)' = A' . B'
- Name
De Morgan's Law 2
- Note
The complement of a product is the sum of the complements.
- Expression
(A . B)' = A' + B'
- Name
Distributive Law
- Note
Multiplication distributes over addition.
- Expression
A . (B + C) = A . B + A . C
Prerequisites
Basic understanding of sets and set operations.
Familiarity with binary number system.
Common mistakes
Confusing AND and OR operations.
Incorrectly applying De Morgan's laws.
Assuming that a simplified Boolean expression directly translates to the minimum number of gates without considering gate types.
Errors in constructing or interpreting truth tables.
Keywords
Boolean Algebra
Logic Gates
AND
OR
NOT
NAND
NOR
XOR
Truth Table
Boolean Laws
Universal Gates
Digital Logic
Practice preview
A 4-to-1 multiplexer has inputs I0, I1, I2, I3 and select lines S1, S0. If S1=1 and S0=0, which input is connected to the output?…
medium
A JK flip-flop is initially in the Q=0 state. If J=1 and K=1, what will be the state of Q after one clock pulse?…
medium
Simplify the Boolean expression F(A, B, C, D) = sum(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15) using K-map.…
medium