business mathematics

Binary and Decimal systems:

What is decimal:
To describe the numbers we generally use the following ten digits.
1,2,3,4,5,6,7,8,9,0.
We know that the system in which we use these ten digits to describe numbers is called decimal system. The decimal system is also called as base ten system.

What is binary:
Only two digits 0 and 1 are used for computation in computers. This system is called BINARY

system. It is also called base two system.

0,1,10,11,100,101,110,111.......and so on are few numbers in binary system.

Binary - Decimal
0 - 0
1 - 1
10 - 2
11 - 3
100 - 4
101 - 5
110 - 6
111 - 7
1000 - 8
1001 - 9

Conversion of Binary to Decimal:
1. convert 1100(base 2) to decimal
1100(2) = 1*8 + 1*4 + 0*2 + 0*1
= 8 + 4 + 0 + 0
= 12


Conversion of Decimal to Binary:
We use division method to convert decimal to binary

Eg:
56 in the binary system:

2 | 56 unit's place
_______
2 | 28-0 two's place
_______
2 | 14-0 fourth's place
_______
2 | 7-0 eighth's place
_______
2 | 3-1 sixteen's place
_______
2 | 1-1 thirty two's place
_______
| 0-1 sixty four's place


Therefore 56 = 111000 (binary)