How to Convert 105 to Binary

Here we will show you step-by-step how to convert the decimal number 105 to binary.

First, note that decimal numbers use 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and binary numbers use only 2 digits (0 and 1).

As we explain the steps to converting 105 to binary, it is important to know the name of the parts of a division problem. In a problem like A divided by B equals C, A is the Dividend, B is the Divisor and C is the Quotient.

The Quotient has two parts. The Whole part and the Fractional part. The Fractional part is also known as the Remainder.

Step 1) Divide 105 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.

Step 2) Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.

Step 3) Repeat Step 2 above until the Whole part is 0.

Step 4) Write down the Remainders in reverse order to get the answer to 105 as a binary.

Here we will show our work so you can follow along:

105 ÷ 2 = 52 with 1 remainder
52 ÷ 2 = 26 with 0 remainder
26 ÷ 2 = 13 with 0 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 remainder
3 ÷ 2 = 1 with 1 remainder
1 ÷ 2 = 0 with 1 remainder

Then, when we put the remainders together in reverse order, we get the answer. The decimal number 105 converted to binary is therefore:

1101001

So what we did on the page was to Convert A₁₀ to B₂, where A is the decimal number 105 and B is the binary number 1101001. Which means that you can display decimal number 105 to binary in mathematical terms as follows:

105₁₀ = 1101001₂

Decimal to Binary Converter
Need another decimal number as a binary number? How to convert 105 to binary is not all we know. Convert another decimal to binary below:

How to Convert 106 to Binary
Here is our next decimal to binary tutorial on our list.