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How to Convert Binary to Decimal

Published: at 05:30 AM

Converting binary to decimal is a common task in computer programming. Binary is a base-2 number system that uses only two digits, 0 and 1. Decimal, on the other hand, is a base-10 number system that uses ten digits, 0 through 9. Converting binary to decimal involves multiplying each digit of the binary number by its corresponding power of 2 and adding up the results.

Conversion

Here’s a step-by-step guide on how to convert binary to decimal:

  1. Choose the binary number you want to convert to decimal.
  2. Write down the powers of 2 from right to left, starting with 202^0.
  3. Multiply each digit of the binary number by its corresponding power of 2.
  4. Add up the results from step 3 to get the decimal value.

Example

Let’s walk through an example to illustrate the process. Suppose we want to convert the binary number 1011 to decimal.

  1. The binary number we want to convert is 1011.
  2. The powers of 2 from right to left are 202^0, 212^1, 222^2, and 232^3
  3. We multiply each digit of the binary number by its corresponding power of 2. The results are: 1×20=11 \times 2^0 = 1, 1×21=21 \times 2^1 = 2, 0×22=00 \times 2^2 = 0, and 1×23=81 \times 2^3 = 8
  4. We add up the results from step 3 to get the decimal value. 1+2+0+8=111 + 2 + 0 + 8 = 11 Therefore, the decimal value of the binary number 1011 is 11.

Binary-Decimal Table

Here’s a table that shows the decimal values of the first 16 binary numbers:

BinaryDecimal
00000
00011
00102
00113
01004
01015
01106
01117
10008
10019
101010
101111
110012
110113
111014
111115

References