How To Convert Number Into Binary Form?

How To Convert Number Into Binary Form?

There are two fundamental methods to convert number into binary. For example, let us convert the number 156₁₀ to binary:

1. Short division by two with remainder: First write the decimal number as the dividend and the base i.e. two as the divisor inside and outside of the upside-down long division symbol respectively.

Write the quotient i.e. 78 under the long division symbol, and the remainder i.e. 0 to the right of the dividend.

Follow the same steps until you reach 0 as quotient. Trace the remainders from bottom to top to get the desired binary number.

2. Descending powers of two and subtraction: From right to left start listing the powers of 2 in a “base 2 table”. Start at 2⁰e. “1”. Each time increment the exponent by one. Continue till you reach a number near to the initial decimal number. Select the biggest number that’ll fit into the number you are converting. The biggest power of two that can fit into 156 is 128. For the left most binary digit write one under its box in the chart. Then, from 156 i.e. your initial number subtract 128. You will have 28. Using 28, the new number, move down your chart denoting how many times every power of 2 can fit into the dividend. Such as, 64 does not go into 28, therefore for the next binary digit to the right write a 0 under its box. Continue till you reach a number that can go into 28. Then, subtract every subsequent number that fits, and mark it as 1. Continue till the chart ends. Voila! You have the binary number as it is from left to right.