Binary system  

Binary system

Objectives

Definition of the Binary system  
How do I convert a decimal number from decimal to binary?


 Define the Binary system  
 A method of representing numbers that has 2 as its base and uses only the digits 0 and 1. Each successive digit represents a power of 2.

For example
10011 = (1 × 24) + (0 × 23) + (0 × 22) + (1 × 21) + (1 × 20)
= 16 + 0 + 0 + 2 + 1
=19


It is very convenient to describe the value of bytes used in computer science. The third numeral system is the binary (or “base 2”) system. It has 2 numerals (0 and 1), and it is used to represent the value of bits – the type of information stored in a computer s memory


How do I convert a binary number to decimal?
The value of any decimal number will be equal to the sum of its digits multiplied by their respective weights. For example:  N = 616310 (Six Thousand One Hundred and Sixty Three)  in a decimal format is equal to:
6000 + 100 + 60 + 3 = 6163
or it can be written reflecting the weight of each digit as:
( 6×1000 ) + ( 1×100 ) + ( 6×10 ) + ( 3×1 ) = 6163
or it can be written in polynomial form as:
( 6×103 ) + ( 1×102 ) + ( 6×101 ) + ( 3×100 ) = 6163
 
Where in this decimal numbering system example, the left most digit is the most significant digit, or MSD, and the right most digit is the least significant digit or LSD. In other words, the digit 6 is the MSD since its left most position carries the most weight, and the number 3 is the LSD as its right most position carries the least weight.