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 Digit8 Bits = 1 Byte1024 Bytes = 1 Kilobyte 1024 Kilobytes = 1 Megabyte 1024 Megabytes = 1 Gigabyte 1024 Gigabytes = 1 Terabyte 1024 Terabytes = 1 Petabyte 1024 Petabytes = 1 Exabyte1024 Exabytes = 1 Zettabyte 1024 Zettabytes = 1 Yottabyte 1024 Yottabytes = Brontobyte1024 Brontobytes = 1 Geopbyte  1 Bit = Binary Digit8 Bits = 1 Byte1000 Bytes = 1 Kilobyte 1000 Kilobytes = 1 Megabyte 1000 Megabytes = 1 Gigabyte 1000 Gigabytes = 1 Terabyte 1000 Terabytes = 1 Petabyte 1000 Petabytes = 1 Exabyte1000 Exabytes = 1 Zettabyte 1000 Zettabytes = 1 Yottabyte 1000 Yottabytes = 1 Brontobyte1000 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 roundoff.
For details refer
Watch Video Lecture on YouTube: Viddeo Tutorial on Binary Numbers
Youtube Video Tutorial on Binary Numbers