# Number Systems Index

## Binary Arithmetic You have to learn addition, subtraction, multiplication and division of binary number. In brain, you have to keep that in the arithmetic of binary number, carry is written in binary (2) just like as 10 is used in decimal system for carry.       Addition of Binary numbers: Follow the following formulae: Example: 1010   first number 1001    second number 10011    Results   Subtraction of Binary Numbers: The subtraction of binary is more interesting, but less complex for novice students, but not fear, jump to...

## Hexadecimal Number system and Their Conversion The number with base 16 is called hexadecimal number. It is denoted by H. It has 16 symbols starting from 0 to 15. The following table shows relationship between hexadecimal and binary numbers. The 4-bit format of binary is used for hexadecimal to binary conversion.     Weighted value: 1048576 65536 4096 256 16 1   Hexadecimal Number...

## Octal Number system and their Conversion The number with base 8 is called octal number. It is represented by Q or O. It was once very popular number system, especially used in the Digital Equipment Corporation PDP/ 8 and other old computers. It is rarely used today. The octal number system has eight symbols starting from 0 to 7.   Weight Value: 32768 4096 512 64 8 1   Octal to Binary and Binary to Octal Conversion: The three digit format of binary digits is used for octal to binary conversion or vice versa.   (a)    Octal to Binary: 3-bits binary...

## Binary to Decimal Conversion Conversion binary to decimal and vice versa: We multiply each binary digit by its weighted position, and add each of the weighted value together.         Weight value: 32 16 8 4 2 1   To convert decimal number into binary number, repeated division by 2 is needed. There is second method is also in which repeated subtraction by the weighted position value are applied. Q. Convert following decimal into binary numbers: (a) (45)10 = (101101)2   Binary to Decimal Conversions:   Q. Convert following...

## Why does Computer understand only binary?

Q.  Why does Computer understand only binary? In computer system all working mechanism depends on switch ON and OFF techniques to read/write data. A SWITCH ON is corresponding to 1 and OFF corresponding O. In this fashion, all data are stored in memory. Input data is converted into digital signals and passes from component to component, and in storing devices (memory or register) it is converted into binary or machine codes. Example: Suppose, we have to write BIKAS, it is heeded 5 byte to store it. When we press letters BIKAS, these letters...

## Data, Information and Knowledge Data, Information and Knowledge are described below individually below: Data: Generally, a raw material for computer is called data. It is a building block of Information. Raw materials have no appropriate meanings. These raw materials are send to computer through input devices.   Example: When we write 18. The 18 is nothing but only data. It has no any particular meaning.   Information: The processed data is called information. Information is a meaningful fact and figure of real life value. We get information in the form of text,...

## Nibble, Byte, word, ASCII, ISCII, and EBCDIC Nibble, Byte, word, ASCII, ISCII, and EBCDIC are explained below: (a)    Nibble: The four bits is called Nibble. BCD (Binary-Coded Decimal) number is expressed in a nibble. Example: 0 0 0 1   (b)   Bytes: The two nibbles or eight bits are called Byte. Example: 1 1 1 0 1 0 0 0   (c) Words: A byte represents one character, so, character count of word is equal to byte numbers. For instance, the word “COMPUTER” has 8 characters so, it is represented by 8 bytes.   (d) ASCII: It stands...

## Binary and Decimal Number System Decimal Number System: The number of base or radix 10 is called decimal numbers. It is a first number system in which all the ancient and modern mathematical calculation is done. Other number of systems is derived from it. Our daily life transaction is done in decimal system. There are many number systems available from which we study only decimal, octal, hexadecimal, and binary systems. The following chart displays relation amongst several number systems:   Binary Number System Binary number is a number of base (radix) 2. It is... 