CSCI 1412 Logic Gates Parminder Kang Email: [email protected] Home: www.cse.dmu.ac.uk/~pkang Phones OFF Please
Jan 15, 2016
CSCI 1412
Logic Gates
Parminder Kang
Email: [email protected]
Home: www.cse.dmu.ac.uk/~pkang
Phones OFF Please
1. Basic Gates
1.1 AND gate:
The AND operation is performed by the AND gate.
Definition:
For two integers A & B;
if A AND B are equal to 1 then the result is 1.
Otherwise the result is 0.
The AND operation is represented by '.' (dot), although the dot is
often omitted in logical expressions.
We write: T=A.B (or T=AB), and say, 'T equals A and B'
The operation of the AND gate is described by the truth table:
A B T
0 0 0
0 1 0
1 0 0
1 1 1
1.2 OR Gate:
The OR operation is performed by the OR gate:
Definition:
For two integers A & B;
if A OR B, OR both are equal to 1 then the result is 1.
Otherwise the result is 0.
The OR operation is represented by '+'
We write: T=A+B , and say, 'T equals A or B'
The operation of the OR gate is described by the truth table:
A B T
0 0 0
0 1 1
1 0 1
1 1 1
1.3 NOT Gate:
The NOT operation is performed by the INVERTER (or NOT gate).
The output of the inverter is the logical inverse of the input.
We write: T=/A, and say, 'T equals not A'.
The operation of the inverter is described by the truth table:
A T
0 1
1 0
Inverters are often appended to AND and OR gates to produce NAND and NOR gates.
A
BT
NAND Gate
A
BT
NOR Gate
1.4 EXCLUSIVE-OR
The EXCLUSIVE-OR operation is performed by the EXCLUSIVE-OR gate:
Definition: For two integers A & B; if A OR B are different then the result is 1.
Otherwise the result is 0.
T=A B ; 'T equals A exclusive or B'
A B T0 0 0
0 1 11 0 11 1 0
A
BT
The EX-OR is a luxury as we don't really need it and we can make it anyway from the other gates. EX-OR is very common so someone decided that we need special symbols for it.
2 Adder:
an adder is a digital circuit that performs addition of numbers.
In modern computers adders reside in the ALU where other operations are performed.
2.1 Half Adder:
A half adder has two inputs, generally labelled A and B, and two outputs, the sum S and carry C.
2.1 Full Adder:
A full adder is a logical circuit that performs an addition operation on three binary digits.
The full adder produces a sum and carry value, which are both binary digits.
Input Output
A B Cin Cout S
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1