Binary number

Procedure to converting a Decimal Number to a Binary Number

1. Firstly, draw a table to illustrate how decimal number is converted to a binary number.

2. Then, determine the greatest power of 2 that is less or equal to the number in decimal that is to be converted to binary number. (X ₁₀≤ 2ⁿ).
3. With the highest power of2, 2ⁿ, compare it with the decimal number. If the place value of 2ⁿ is smaller than the decimal number, place ‘1’ in that column.
4. Then, subtract the value of 2ⁿ from the decimal number.
5. The left value is used and the same procedure followed but this time the left over value is compared with the value of 2^n-1.
6. ‘1’ is place in the column if the left value is greater than the value 2^n-1. If it is not, place ‘0’.
7. The same procedure repeated until the left over value is 0.
8. Now, decimal number is converted to binary number.

Example

Convert (55)₁₀to binary number.

2. The greatest power of 2 that is less than (55)₁₀ is 2⁵=32.
3. Since 32 is less than 55, so ‘1’ is place in the column.
4. 32 is subtracted from 55 will be 23. The left over value is 23.
5. 23 is compared with 2⁴=16. 16 is less than 23, so ‘1’ is place in the column. 16 is subtracted from 23 will get 7. The left over value is 7.
6. 7 is compared with 2³=8. 8 is bigger than 7 so ‘0’ is place in the column. The left value is still 7 since it cannot be subtracted with 8.
7. 7 is compared with 2²=4. 4 is smaller than 7, so ‘1’ is place in the column and 4 is subtracted from 7. The left value will be 3.
8. 3 is compared with 2¹=2. 2 is smaller than 3 and ‘1’ is place in the column. The left over will be 1 and compared with 2⁰=1. 1 is subtracted from 1. Finally the left over value is 0 and the procedure is done.
9. The table shall be like this.