**Digital systems are based on two logic levels which are usually represented as 1's and 0's.We need different ways to combine different logical signals or conditions to provide a logical result,**

**LOGIC GATES**

**Overview on Digital Logic:**

Digital (or Boolean) logic is that the description of binary values through printed circuit board (PCB) technology that uses circuits and digital logic gates to line up the implementation of basic computer operations. Digital logic is an ordinary part of electrical engineering (EE) and design/style courses. Furthermore, it is the support for digital computing and provides a basic understanding on how circuits and hardware communicate within a computer. Combinations of logic gates used in digital logic, form circuits which will perform specific tasks within larger circuits or systems. The process of manufacturing complex circuits using combinations of basic devices is named Combinational Logic.

*Logic gate is an elementary building block of a digital circuit . Most logic gates have two inputs and one output. At any given moment, every terminal is in one of the two binary conditions represented by different voltage levels : low (0) or high (1).*

e.g., consider the logical statement: "If I move the switch on the wall up, the light will turn on" At first glance, this seems to be a correct statement. However looking at a few other factors, it is realized that there'smore to it than this. In this example, a more complete statement would be: "I f I move the switch on the wall up and the light bulb is good and the power is on, the light will turn on."

If these two statements are logical expressions and use logical terminology, first statement can be reduced to:

Light = Switch

This means nothing more than that the light will follow the action of the switch, so that when the switch is up/on/true/1, the lightwill also be on/true/1. Conversely, if the switchis down/off/false/0, the lightwill also be off/false/0.

For second version of the statement, a slightly more complex expression is combine the separate variables of Switch, Bulb, and Power in this expression. The symbol normally used is a dot,which is the same symbol used for multiplication in some mathematical expressions.

Using this symbol, three-variable expression becomes.

Light = Switch • Bulb• Power

Light = Switch and Bulb and Power

Normally, symbols are used rather than words to designate the and function that are used to

Generally logic state of a terminal can, and does, change often, as the circuit processes data. In most logic gates, the low state is approximately zero volts (0 V), while high state is approximately five volts positive (+5V).* *

*There are seven basic logic gates : *

*1. AND *

*2. OR *

*3. XOR *

*4. NOT *

*5. NOR*

*6.NAND*

*7.XNOR*

Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arrayed together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space. Arrays of logic gates are found in digital integrated circuits (!Cs).As IC technology advances, the required physical volume for each individual logic gate decreases and digital devices of the same or smaller size become capable of performing ever-morecomplicated operations at ever-increasing speed.

**UNIVERSAL GATES**

Universal gates are the ones which can be used for implementing any gate like AND, OR and NOT or any combination of these basic gates;NAND and NOR gates are universal gates; but there are some rules that need to be followed when implementing NAND or NOR based gates.

**BOOLEAN EXPRESSIONS**

Digital circuits use ON-OFF devices to implement operations of a system of logic called two-valued using Boolean expression. The statements may take the form of algebraic expressions, logic block diagrams, or truth tables, aswell as circuits. Boolean expression is composed of variables and terms. The simplification of Boolean expressions can lead to more effective computer programs, algorithms and circuits.

**FORMS OF BOOLEAN EXPRESSIONS.**

(1) Sum of Product form (SOP)

e.g. W = ( X Y Z ) + ( X Y Z ) + ( X Y Z)

Each term in such an expression is called minterm.

(2) Product of Sum form (POS)

e.g. S = (P + Q + R) (P + Q + R) (P + Q + R)

Each term in such an expression is called maxterm.

**Minterm and Maxterm**

n variables can be combined to form 2" minterms or maxterms.

Each minterm is obtained from an AND term of n variables with each variable being primed, if corresponding bit of binary number is 0 and unprimed,bit is 1.

Each maxterm is obtained from an OR term of n variables with each variable being unprimed, if corresponding bit is a 0 and primed bit is 1.

Maxterm is complement of its corresponding minterm and vice versa.

**MINIMlZATION OF BOOLEAN EXPRESSION.**

(1) Convert equation from POS form to SOP form.

(2) Remove parenthesis if any in the expression.

(3) If there are two or more identical terms, keep only one of them and drop the other.

(4) Ifa variable and its complements are present in a term, reduce it to 0. (A. A= 0).

(5) Group two terms of which one contains a variable and other its complement, except for which both are identical. They can be reduced to a single term and in the reduced term, above variable will be absent

(C + c = 1)

e.g. (A . B . C ) + (A. B. C) = A. B ( C + C) = A . B

(6) If there are two terms which are identical except that one contains an extra variable, reduce them into a single term by dropping the larger one.

e.g. B.C + A . B . C = B . C (1 + A ) = B . C (1) = B

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Boolean algebra Rules, Combinational and sequential logic circuits, Definition of Minimization, Introduction of Number representations and computer arithmetic (fixed and floating point) **A main component of digital logic consists of 5 different logic gates:** AND OR XOR NAND NOR These basic logic gates are utilized in conjunction with each other to create elaborate engineering designs that deliver various computing outcomes. There are some ways that a number of logic gates can be combined to perform a selected task. They may all work, but some combinations will perform the task that better than others. For example, a circuit designer might want to design a combinational logic circuit that uses the minimum number of gates, or performs the specified task within the least time, or at the minimum cost.

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