# Useful Number Systems for Computers for IAS

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## Name Base Digits

- binary 2: 0,1
- octal 8: 0, 1, 2, 3, 4,5, 6,7
- decimal 10: 0, 1, 2, 3, 4, 5, 6,7, 8,9
- hexadecimal 16: 0, 1, 2, 3, 4, 5, 6, 7,8, 9, A, B, C, D, E, F

## Useful Number Systems for Computers

Name | Base | Digits |

Dual binary | 2 | 0,1 |

Octal | 8 | 0, 1, 2, 3, 4,5, 6,7 |

Decimal | 10 | 0, 1, 2, 3, 4, 5, 6,7, 8,9 |

Hexadecimal | 16 | 0, 1, 2, 3, 4, 5, 6, 7,8, 9, A, B, C, D, E, F |

- Binary Number System
- Decimal Number System
- Octal Number System
- Hexadecimal Number System
- Conversion of Rational Numbers
- Binary Arithmetic
- Addition
- Subtraction
- Multiplication

Processor or Virtual Storage | Disk Storage |

1 Bit = Binary Digit 8 Bits = 1 Byte 1024 Bytes = 1 Kilobyte 1024 Kilobytes = 1 Megabyte 1024 Megabytes = 1 Gigabyte 1024 Gigabytes = 1 Terabyte 1024 Terabytes = 1 Petabyte 1024 Petabytes = 1 Exabyte 1024 Exabytes = 1 Zettabyte 1024 Zettabytes = 1 Yottabyte 1024 Yottabytes = Brontobyte 1024 Brontobytes = 1 Geopbyte | 1 Bit = Binary Digit 8 Bits = 1 Byte 1000 Bytes = 1 Kilobyte 1000 Kilobytes = 1 Megabyte 1000 Megabytes = 1 Gigabyte 1000 Gigabytes = 1 Terabyte 1000 Terabytes = 1 Petabyte 1000 Petabytes = 1 Exabyte 1000 Exabytes = 1 Zettabyte 1000 Zettabytes = 1 Yottabyte 1000 Yottabytes = 1 Brontobyte 1000 Brontobytes = 1 Geopbyte |

## Binary Data Representation

- Computers store all data as patterns of 0՚s and 1՚s. Information systems using 0՚s and 1՚s are collectively known as
*binary information systems*. - Each 0 or 1 in a binary value is called a
*bit*, which is short for*binary digit*. - A collection of 8 bits is called a
*byte*. A byte is a very common unit of storage for electronic memory. It is usually the smallest chunk of data that programs process, although many languages support processing individual bits as well. Processing data smaller than a byte is generally not as easy as processing whole bytes. - A collection of 4 bits is called a
*nybble*. - A
*word*is the maximum amount of data a CPU can process at once, and is usually 1,2, 4, or 8 bytes (8 to 64 bits) . - Numeric data is stored using several different binary number formats, all of which use a finite number of
*binary digits (bits)*, and therefore are subject to overflow and round-off.

For details refer