What is 100 in binary?

Steps to Solve

1. Divide the decimal number by 2 Start with the decimal number 100. Divide it by 2 and write down the quotient and the remainder.

For example: $$ 100 \div 2 = 50 , \text{(quotient)}, \quad 100 \mod 2 = 0 , \text{(remainder)} $$

2. Repeat the process with the quotient Take the quotient (50) and divide it again by 2. Continue to write down the new quotient and the remainder.

For example: $$ 50 \div 2 = 25 , \text{(quotient)}, \quad 50 \mod 2 = 0 , \text{(remainder)} $$

3. Continue until the quotient is 0 Repeat this division process until the quotient becomes 0. The subsequent steps will look like this:

$$ 25 \div 2 = 12 , \text{(remainder = 1)} $$

$$ 12 \div 2 = 6 , \text{(remainder = 0)} $$

$$ 6 \div 2 = 3 , \text{(remainder = 0)} $$

$$ 3 \div 2 = 1 , \text{(remainder = 1)} $$

$$ 1 \div 2 = 0 , \text{(remainder = 1)} $$

4. Collect the remainders Now, collect all the remainders from the divisions, starting from the last remainder obtained to the first. This gives the binary representation.

From the above steps, we collected the remainders: 1 (from last division), 1, 0, 0, 1, 0, 0

5. Write the binary number Finally, write down the remainders in reverse order. The binary representation of decimal 100 is:

$$ 1100100_2 $$