How to convert decimal to binary

Converting a decimal number to binary involves dividing the decimal number by 2 repeatedly and keeping track of the remainders at each step. Here’s a step-by-step mathematical method to convert a decimal number to binary:

Let’s say you have a decimal number “N” that you want to convert to binary.

• Start by dividing the decimal number “N” by 2.
• Note down the quotient and remainder.
• Use the quotient obtained in the previous step and repeat steps 1 and 2 until the quotient becomes 0.
• The binary equivalent of the decimal number “N” is the sequence of remainders obtained in reverse order.

Conversion Process

Let’s say we have decimal number N = 13.

• N = 13, Divide N by 2: Quotient = 6, Remainder = 1
• N = 6, Divide N by 2: Quotient = 3, Remainder = 0
• N = 3, Divide N by 2: Quotient = 1, Remainder = 1
• N = 1, Divide N by 2: Quotient = 0, Remainder = 1

Now, we take the remainders in reverse order: 1101.

So, the binary representation of decimal number 13 is 1101.

Solved Example

Example 1 – Convert 13₁₀ to binary

Ans. So, 13₁₀ = 1101₂

Example 2- Convert 174₁₀ to binary

Ans. So, 174₁₀ = 10101110₂

FAQs on decimal to binary

How do you convert 0.75 to binary?

0.75 * 2 = 1.5 → Write down 1. 0.5 * 2 = 1.0 → Write down 1. 0.0 * 2 = 0.0 → Stop. So, the binary representation of 0.75 is 0.11.

How do you convert binary digits to decimals?

To convert binary digits to decimals, follow these steps: Start from the leftmost binary digit. Multiply each binary digit by 2 raised to the power of its position (counting from 0 for the rightmost digit). Sum up all the products obtained in step 2.

What is 128 decimal in binary?

Decimal 128 is equivalent to binary 10000000.

How do you write 1024 in binary?

To write decimal 1024 in binary: Divide 1024 by 2 repeatedly until the quotient becomes 0. Write down the remainders in reverse order. o, decimal 1024 is equivalent to binary 10000000000.

What binary number is 11110000?

Binary number 11110000 in decimal is equivalent to 240.