DIGITAL LOGIC GATESAND BOOLEAN ALGEBRA Dr. C. SARITHA LECTURER IN ELECTRONICS SSBN DEGREE & PG COLLEGE ANANTAPUR
LOGIC GATESINTRODUCTION: A logic gate is an electronic circuit/device which makes logic decisions. Most logic gates are two inputs and one outputs. At any given moment, every terminal is in one of the two binary conditions low (0) or high(1), represented by different voltage levels.
The logic state of a terminal can, and generally does, change often as the circuit processes data. In most logic gates, the low state is approximately 0v, while the high state is approximately 5v. Logic gates are also called as switches. with the advent of integrate circuits, switches have been replaced by TTL circuit and CMOS circuits. symbolic logic uses values, variables and operations.
TYPES OF LOGIC GATES:The most common logic gates used are,Basic gates1.OR2.AND3.NOTUniversal gates1.NAND2.NOR X-OR or Exclusive-OR
OR GATE: The OR gate has two or more inputs and one output. Its output is true if at least one input is true.SYMBOL:
The OR operation may be defined as “Y equals A OR B”. Y=A+B Where, the symbol ‘+’ indicates the OR concept. Each terminal may assume two possible values either zero or one.
NOT GATE or Inverter Gate: A NOT gate is a basic gate that has one input and one output.SYMBOL:
The NOT circuit serves to invert the polarity of any input pulse apply to it. If A is the input then output “Y equals to NOT A or Ā. Y= Ā Where, the bar symbol over A represents NOT or compliment operation
Exclusive OR or X-OR GATE: The X-OR gate is a logic gate having two inputs with and single output.SYMBOL:
The Boolean expression for the X-OR gate is given by, Y=A+B+ Where + indicates the exclusive OR + operation and in terms of expression it can be expanded as Y=AB+AB
TRUTH TABLE: A B AB+AB 0 0 0 0 1 1 1 0 1 1 1 0
ADVANTAGES OF LOGIC GATES: It is generally very easy to reliably distinguish between logic 1 or logic 0. The simplest flip-flop is the RS which is made up of two gates. K-map is also designed by using logic gates. That simplification helps when you start to connect gates to implement the functions. These gates are also used in TTL and CMOS circuitary.
BOOLEAN ALGEBRA Boolean Algebra derives its name from the mathematician George Boole in 1854 in his book “An investigation of the laws of taught”. Instead of usual algebra of numbers Boolean algebra is the algebra of truth values 0 or 1. In order to fully understand this the relation between the AND gate, OR gate & NOT gate operations should be appreciated.
POSTULATES OF BOOLEAN ALGEBRA: The Boolean algebra has its own set of fundamental laws which differ from the ordinary algebra. They are,OR laws: A+0=A A+1=1 A+A=A A+Ā=1
AND laws: A.0=0 A.A=A A.1=A A.Ā=0NOT laws: 0=1 1=0 If A=0 then Ā=1 If A=1 then Ā=0 Ā=A
Advantages: If we use Boolean algebra for your logical problem you can save more gates and operations. so your design will be cheaper, more comprehensible, more serviceable . It allows logical steps quickly and repeatedly.Disadvantages: Can only arrive at direct results not implied once.