Number System In Computer

Number System In Computer

Number System

A computer is a man-made electronic device. It does not have its own intelligence but is capable of carrying out different operations. The operation of the computer is based on certain principles, methods, and logic. This deals with the conceptual aspect of data representation within the computer and conversion among binary, octal, and hexadecimal number systems.

In modern computers, memory and processing units are made up of a set of silicon chips, each of them containing a large number of transistors, A transistor is a two-state device like a switch having an OFF state and an ON state. The OFF state can be represented by 0 and the ON state is represented by 1. These 0 and 1 are called Binary Digits or BITS. Thus, a computer does not understand anything other than 0 and 1 i.e. computer circuits can respond only to the binary state. So data and program must be coded in a binary form before it goes into the computer.

ON    OFF   ON    OFF   ON    OFF   ON   OFF

1        0        1         0        1         0        1       0

The collection of eight such switches each representing a bit is called a Byte.

i. e. 8 bits = 1 byte

A byte is equivalent to one ASCII character i.e. a number, a letter, a mathematical symbol, or a punctuation mark.

Binary Coding

The normal character (alphabet, number, etc.) as we know has to be broken down to a set of simple codes, so a computer can understand it. All the characters have been coded for the sake of easy exchange of information between the different systems and to make communication possible between users and the machine. ASCII (American Standard Code for Information Interchange) coding system specifies all the lower and upper case letters, numbers, punctuation symbols, and special control commands. The system uses 8 bits to code each character, the first 7 bits represent the character and the eighth bit (called parity bit) enables the computer to check the information we have put in. A maximum of 256 characters can be coded under the ASCII coding system.

For example, the ASCII code for A = 65 when A is pressed the binary equivalent of 65 i.e. 1000001 is transmitted as pulses.

 Digit: A single character in a numbering system or counting system having a specific radix or base.

Bit, Nibble, Byte, and Computer Word 

Computers do not understand normal alphabets and numbers in the form we understand. It has to be broken down into computer understandable code with the help of a coding system so that communication between the user and computer is possible. Previously, computers were based on EBCDIC (Extended Binary Coded Decimal Interchange Code) coding system (eight bits coding system), but most of the modern computers are based on ASCII (American Standard Code for Information Interchange) coding system. ASCII coding system uses 7 bits to represent a character or a number and one bit is added before seven bits to form eight bits code. The additional bit is called the parity bit. The parity bit allows the computer to double-check the information we have input in.

Bit: It stands for Binary digiT. A single digit in a binary number a 0 or 1 is called a bit. Within the computer, a bit is physically a memory cell, a magnetic spot on a disk or tape, which can represent a binary state (0 or 1). 

Nibble: It is a combination of four bits i.e. one Nibble consists of four bits. 

Example: 0101 is one Nibble.

Byte:  It is a common unit of computer storage. It is made up of eight bits. 

Byte: Example: 01001101 is one byte. 

Computer Word:

It is the computer's internal storage unit that refers to the number of bits the computer uses for processing at one time. It differs from computer to computer. 

FOR example, A 16-bit computer processes two bytes at the same time i.e it uses two bytes of words. A 32-bit computer processes four bytes at a time, so the word length for that computer is four bytes.

Binary to Hexadecimal Conversion 

The method for conversion of a binary number to hexadecimal number is similar to that of conversion of a binary number to octal number except the grouping is done using four bits as the hexadecimal digit is represented in terms of four bits.

Hexadecimal to Binary Conversion

The method for conversion of hexadecimal number to binary number is similar to that of conversion of octal number to binary number except for the binary representation of each hexadecimal digit is done in terms of four bits.

Octal to Hexadecimal Conversion 

An octal number can be converted into its equivalent hexadecimal number by, first converting to binary and then the decimal equivalent to hexadecimal number.

Hexadecimal to Octal Conversion

A hexadecimal number can be converted into its equivalent octal number by, first converting to binary and then the binary equivalent to octal number, or first converting to decimal and then the decimal equivalent to hexadecimal number.

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