All of us are familiar with the decimal number system because this is the number system we use in our everyday life. The basic digits used in decimal system are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Number greater than 9 are written as suitable combination of these digits. The base of this number system is 10.

In binary system of numbers have only two digits, 0 and 1 are used. This system find may applications in digital computers. Whenever an operator enters a decimal number into a digital computer, the computer must convert the number into the binary form this is nothing but decimal to binary conversion. In this section we will learn more about decimal to binary conversion.

To convert a decimal number into its binary equivalent, the decimal number is expressed as a sum of ascending power of 2. The successive coefficient of the power of 2 represent the number in the binary system.
Thus, to convert the decimal number 9 to its binary form, we can write
$9$ = $8 + 1$ = $1 \times 2^{3}+ 0 \times 2^{2}+ 0 \times 2^{1}+1 \times 2^{0}$
The coefficient of 2^{3}, 2^{2}, 2^{1}and 2^{0} are 1, 0, 0 and 1 respectively. Hence the binary representation of 9 is 1001 (one-zero-zero-one).

Alternative method of converting from the decimal to binary system is to divide the decimal number progressively by 2 till the quotient is zero. The remainder of the successive divisions, written in the reverse order, give the binary number. For example convert the decimal 11

2|11 ; remainder 1
2| 5 ; remainder 1
2| 2 ; remainder 0
2| 1 : remainder 1
0
Arranging the remainder in reverse order, i.e., from bottom to up we can write the binary equivalent of 11 as 1011(one-zero-one-one).
The following are the example for decimal to binary conversion.

Solved Examples

Question 1: Find the binary equivalent of 143
Solution:
 

2 |143 ...1
2 | 71  ...1
2 | 35  ...1
2 | 17  ...1
2 | 8    ...0
2 | 4     ...0
2 |2     ...0
   | 1     ...1
 
The binary equivalent of 143 is 10001111

 

Question 2: Convert 121 to equivalent binary number
Solution:
 
2 | 121 ...1
2 | 60   ...0
2 | 30  ...0
2 | 15  ...1
2 |  7   ...1
2 | 3    ...1
2 | 1    ...1
0

The binary equivalent of 121 is 01111001

 

Question 3: Find the binary equivalent of 99?
Solution:
 
2 | 99 ….1 
2 | 49  ….1
2 | 24  ….0
2 | 12  ….0
2 | 6  ….0
2 | 3  ….1
2 | 1  ….1
0

The binary equivalent of 99 is 01100011