Computer science notes, Thesis of Applications of Computer Sciences

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Computer Fundaments

Unit-I

Mrs. Kiran Bala Dubey Assistant Professor Department of Computer Science Govt. N. P. G. College of Science, Raipur

Number System

• Decimal number system
• Binary number system
• octal number system
• Hexa decimal number system
• ASCII
• EBCDIC
• Gray code
• BCD

EBCDIC

• EBCDIC, in fullextended binary-coded decimal interchange code., Data-encoding system, developed by IBM, that uses a unique eight-bit binary code for each number and alphabetic character as well as punctuation marks and accented letters and non-alphabetic characters.
• EBCDIC differs in several respects from ASCII, the most widely used system of encoding text, dividing the eight bits for each character into two four-bit zones, with one zone indicating the type of character, digit, punctuation mark, lowercase letter, capital letter, and so on, and the other zone indicating the value (that is, the specific character within this type).

Gray code

• Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
• Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers.
• Gray code is not weighted that means it does not depends on positional value of digit. This cyclic variable code that means every transition from one value to the next value involves only one bit change.
• Gray code also known as reflected binary code, because the first (n/ 2 ) values compare with those of the last (n/ 2 ) values, but in reverse order.

BCD

• Binary Coded Decimal or BCD is simply the 4-bit binary code representation of a decimal digit with each decimal digit replaced in the integer and fractional parts with its binary equivalent. BCD Code uses four bits to represent the 10 decimal digits of 0 to 9.

Binary Addition

Eg. 2’s complement of binary number 110010 is 1

001101 ------------>(1’s complement of 110010)

001110 ------------>(2’s complement of 110010)

Logic Gates

Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic. Based on this, logic gates are named as -

• AND gate
• OR gate
• NOT gate
• NOR gate
• NAND gate
• XOR gate

The OR gate is an electronic circuit that gives a high output (1) if

one or more of its inputs are high. A plus (+) is used to show the

OR operation.

A circuit which performs an OR operation is shown in figure -

Logic diagram A + B = Y Truth Table

The NOT gate is an electronic circuit that produces an inverted

version of the input at its output.NOT gate is also known as

Inverter. It has one input A and one output Y.

Logic diagram Truth Table

This is a NOT-OR gate which is equal to an OR gate followed by a

NOT gate. The outputs of all NOR gates are low if any of the

inputs are high.

The symbol is an OR gate with a small circle on the output. The

small circle represents inversion.

Logic diagram Truth Table

The exclusive-OR gate is abbreviated as EX-OR gate or sometime

as X-OR gate.The 'Exclusive-OR' gate is a circuit which will give a

high output if either, but not both, of its two inputs are high.

XOR or Ex-OR gate is a special type of gate. It can be used in the

half adder, full adder and subtractor.

Logic diagram Truth Table