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2.1.12 Construct truth tables using the above operators.
2.1.13 Construct a logic diagram using AND, OR, NOT, NAND, NOR and XOR gates.
2.1.11 Define the Boolean operators: AND, OR, NOT, NAND, NOR and XOR.
Behaviour of Gates and Circuits can be described
Behaviour of Gates and Circuits can be described
Gates and Circuits
Gates and Circuits
Gate
Gate
A device that performs a basic operation on electrical signals
Circuits
Circuits
Gates combined to perform more complicated tasks
Boolean expressions
Boolean expressions
Uses Boolean algebra, a mathematical notation for expressing two-valued logic
Logic diagrams
Logic diagrams
A graphical representation of a circuit
Each gate has its own symbol
Truth tables
Truth tables
A table showing all possible input values and the associated output values
Gates, Boolean Expression, Logic Diagram, Truth Table
Gates, Boolean Expression, Logic Diagram, Truth Table
NOT Gate
NOT Gate
A NOT gate accepts one input signal (0 or 1) and returns the complementary (opposite) signal as output
NOT Gate in Java
NOT Gate in Java
The example code reverses the value of a using the (!) NOT operator
What is the output of the code segment?
boolean a = true;
boolean x = !a;
System.out.println(x);
AND Gate
AND Gate
An AND gate accepts two input signals
If both are 1, the output is 1; otherwise,
the output is 0
AND Gate in Java
AND Gate in Java
The example code evaluates values of a and b using the AND (&&) operator.
What is the output of the code segment?
boolean a = true;
boolean b = false;
boolean x = a && b;
System.out.println(x);
OR Gate
OR Gate
An OR gate accepts two input signals
If both are 0, the output is 0; otherwise,
the output is 1
OR Gate in Java
OR Gate in Java
The example code evaluates values of a and b using the OR (||) operator.
What is the output of the code segment?
boolean a = true;
boolean b = false;
boolean x = a || b;
System.out.println(x);
XOR Gate
XOR Gate
An XOR gate accepts two input signals
If both are the same, the output is 0; otherwise, the output is 1
XOR Gate in Java
XOR Gate in Java
The example code evaluates values of a and b using the XOR (^) operator.
What is the output of the code segment?
boolean a = true;
boolean b = false;
boolean x = a ^ b;
System.out.println(x);
NAND Gate
NAND Gate
The NAND (“NOT of AND”) gate accepts two input signals
If both are 1, the output is 0; otherwise,
the output is 1
NAND Gate in Java
NAND Gate in Java
The example code evaluates values of a and b using the AND !(a && b) operator.
What is the output of the code segment?
boolean a = true;
boolean b = false;
boolean x = !(a && b);
System.out.println(x);
NOR Gate
NOR Gate
The NOR (“NOT of OR”) gate accepts two inputs
If both are 0, the output is 1; otherwise,
the output is 0
NOR Gate in Java
NOR Gate in Java
The example code evaluates values of a and b using the AND !(a || B) operator.
What is the output of the code segment?
boolean a = true;
boolean b = false;
boolean x = !(a || b);
System.out.println(x);
Three-input Gate
Three-input Gate
Some gates can be generalized to accept three or more input values
A three-input AND gate, for example, produces an output of 1 only if all input values are 1
Summary of Gates Behaviour
Summary of Gates Behaviour
NOT - Inverts its single input
AND - Produces 1 if all input values are 1
OR - Produces 0 if all input values are 0
XOR - Produces 0 if both input values are the same
NAND - Produces 0 if all input values are 1
NOR - Produces 1 if all input values are 0
More Examples of Circuits
More Examples of Circuits
X = (A * B)’ * (B + C) * C’
X = (A * B)’ * (B + C) * C’
int X = !(A && B) && (B || C) && !C;
X = (A + B) + (B’ ⊕ C )
X = (A + B) + (B’ ⊕ C )
int X = (A || B) || (!B ^ C);
X = A’ ⊕ (B * C)’
X = A’ ⊕ (B * C)’
int X = !A ^ !(B && C);
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