How to Convert 10400 to Binary

Here we will show you step-by-step how to convert the decimal number 10400 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 10400 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 10400 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 10400 as a binary.

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

10400 ÷ 2 = 5200 with 0 remainder
5200 ÷ 2 = 2600 with 0 remainder
2600 ÷ 2 = 1300 with 0 remainder
1300 ÷ 2 = 650 with 0 remainder
650 ÷ 2 = 325 with 0 remainder
325 ÷ 2 = 162 with 1 remainder
162 ÷ 2 = 81 with 0 remainder
81 ÷ 2 = 40 with 1 remainder
40 ÷ 2 = 20 with 0 remainder
20 ÷ 2 = 10 with 0 remainder
10 ÷ 2 = 5 with 0 remainder
5 ÷ 2 = 2 with 1 remainder
2 ÷ 2 = 1 with 0 remainder
1 ÷ 2 = 0 with 1 remainder

Then, when we put the remainders together in reverse order, we get the answer. The decimal number 10400 converted to binary is therefore:

10100010100000

So what we did on the page was to Convert A₁₀ to B₂, where A is the decimal number 10400 and B is the binary number 10100010100000. Which means that you can display decimal number 10400 to binary in mathematical terms as follows:

10400₁₀ = 10100010100000₂

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