# Fundamental Digital Electronics/Number Base System

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## Number of Base Two

Base two numbers only use the two digits 0 and 1 . Any number greater than 1 is represented by a series of 0 and 1 digits

$1110 = 1 x 2^3 + 1 x 2^2 + 1 x 2^1 + 0 x 2^0$ = 14

Numbers that contain only two digit 0 and 1 are called Binary Numbers. Each 0 or 1 is called a Bit, from binary digit. A binary number of 4 bits is called a Nibble. A binary number of 8 bits is called a Byte. A binary number of 16 bits is called a Word on some systems, on others a 32-bit number is called a Word while a 16-bit number is called a Halfword.

Using 2 bit 0 and 1 to form

a binary number of 1 bit, there are 2 such numbers 0 and 1
a binary number of 2 bit, there are 4 such numbers 00, 01, 10, 11
a binary number of 3 bit, there are 8 such numbers 000, 001, 010, 011, 100, 101, 110, 111
a binary number of 4 bit, there are 16 such numbers 0000, 0010, 0100, 0110, 1000, 1010, 1100, ..., 1111

Therefore , using n bits there are 2n binary numbers of n bits

## Numbers of Base Ten

Base ten numbers use ten digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Any number greater than 9 is represented by a series of digits in the 0 through 9 range.

$14 = 1 x 10^1 + 4 x 10^0$

## Communication (Conversion) between numbers of Different base

The same number 14 expressed

in base ten is 14
in base two is 1110 .

Hence , any number in our base ten system can be represented by a binary number of certain bit