Binary and decimal are two ways of writing the same number

Binary uses only two digits: 0 and 1. Decimal uses ten digits: 0 through 9. When you convert binary to decimal, you are translating from one number system to the other. The number stays the same—only the way you write it changes. For example, the binary number 1010 and the decimal number 10 represent the same quantity.

Every position in a binary number has a value based on powers of 2. The rightmost position is worth 2 to the power of 0 (which equals 1). The next position to the left is worth 2 to the power of 1 (which equals 2). Then 2 to the power of 2 (which equals 4), then 8, then 16, and so on, doubling each time you move left.

To convert, you multiply each binary digit by its position value, then add all those results together. That sum is your decimal number.

Key Takeaways

  • Each position in a binary number represents a power of 2, starting with 2⁰ = 1 on the right and doubling as you move left.
  • Multiply each binary digit (0 or 1) by its position value, then add all the results to get the decimal number.
  • A binary digit in a position is only counted if it is a 1; a 0 in any position contributes nothing to the sum.
  • You can check your work by converting the decimal answer back to binary using repeated division by 2.

Set up the position values for your binary number

Write your binary number across the top of a line. Below each digit, write the position value it represents. Start from the right with 1, then move left writing 2, 4, 8, 16, 32, 64, 128, and so on—each one double the last.

For example, if your binary number is 11010, set it up like this:

Binary digit11010
Position value168421

The position values are powers of 2. The rightmost column is 2⁰ = 1. The next is 2¹ = 2. Then 2² = 4, 2³ = 8, 2⁴ = 16, and so on.

Multiply each digit by its position value

For each column, multiply the binary digit by the position value below it. If the binary digit is 0, the result is always 0. If the binary digit is 1, the result is the position value itself.

Using the example 11010:

  • Leftmost: 1 × 16 = 16
  • Next: 1 × 8 = 8
  • Middle: 0 × 4 = 0
  • Next: 1 × 2 = 2
  • Rightmost: 0 × 1 = 0

You only need to add the position values where the binary digit is 1. The zeros do not contribute anything, so you can skip them if you want to work faster.

Add all the results together

Sum all the products from the previous step. This total is your decimal number.

For 11010: 16 + 8 + 0 + 2 + 0 = 26

So the binary number 11010 equals 26 in decimal. You can verify this by counting: binary 11010 means "one 16, one 8, zero 4s, one 2, and zero 1s"—which adds to 26.

Work through a longer example step by step

Let's convert the binary number 10110101 to decimal. First, write the position values under each digit:

Binary digit10110101
Position value1286432168421

Now multiply and add only the columns with a 1:

  • 1 × 128 = 128
  • 1 × 32 = 32
  • 1 × 16 = 16
  • 1 × 4 = 4
  • 1 × 1 = 1

Total: 128 + 32 + 16 + 4 + 1 = 181. The binary number 10110101 equals 181 in decimal.

Check your answer by converting back to binary

To verify your decimal answer, convert it back to binary using repeated division by 2. Divide the decimal number by 2 and write down the remainder (either 0 or 1). Keep dividing the result by 2 until you reach 0. Then read the remainders from bottom to top.

For example, to check that 26 in decimal is 11010 in binary:

  • 26 ÷ 2 = 13 remainder 0
  • 13 ÷ 2 = 6 remainder 1
  • 6 ÷ 2 = 3 remainder 0
  • 3 ÷ 2 = 1 remainder 1
  • 1 ÷ 2 = 0 remainder 1

Read the remainders from bottom to top: 11010. This matches your original binary number, so your conversion is correct.

Frequently Asked Questions

What if my binary number has 8 digits or more?

The method stays the same. Write out the position values for each digit—they keep doubling as you move left. For an 8-digit binary number, the leftmost position is worth 128. For 16 digits, it is worth 32,768. Multiply each digit by its position value and add the results.

Do I have to memorize the powers of 2?

No. You can write them out each time, or use a calculator. The pattern is straightforward: start with 1 on the right and double each time you move left. After a few conversions, the common ones (1, 2, 4, 8, 16, 32, 64, 128) become familiar.

What if the binary number is just 1 or 0?

Binary 1 equals decimal 1. Binary 0 equals decimal 0. Any binary number that is all zeros equals decimal 0. A binary number that is a single 1 in any position equals the position value of that 1.

Can I use a calculator to convert binary to decimal?

Yes. Most scientific calculators have a binary-to-decimal conversion function. On Windows, the Calculator app in Programmer mode lets you type a binary number and switch the display to decimal. Online converters also work, but learning the method yourself helps you understand how number systems work.