# Binary to Decimal

Convert binary numbers to decimal easily with our Binary to Decimal Converter. Perfect for programming and data analysis, ensuring accurate conversions.

**Binary Number:**A binary number is a base-two numeral system using only two symbols: 0 and 1. It represents quantities using powers of 2.

**Binary Number Example:**An example of a binary number is 10110. Here, the leftmost digit represents 2^4 (16), followed by 2^3 (8), 2^2 (4), 2^1 (2), and 2^0 (1). Adding these powers corresponding to the positions where 1s occur gives the decimal value of the binary number.

**Decimal Number:**A decimal number is a base-ten numeral system that uses ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It represents quantities using powers of 10.

**Decimal Number Example:**Consider the decimal number 456. Here, 4 is in the hundreds place (10^2), 5 is in the tens place (10^1), and 6 is in the ones place (10^0).

**Conversion Process: Binary to Decimal**

**Write the Binary Number:**Start with the given binary number.**Assign Powers of 2:**Assign powers of 2 to each digit from right to left, starting with 2^0 for the rightmost digit.**Multiply and Sum:**Multiply each binary digit by its corresponding power of 2 and sum all these products to get the decimal equivalent.

**Example: Convert Binary 10101 to Decimal**

Binary Number: 10101

Assign Powers of 2:

1 * 2^4 (16) = 16

0 * 2^3 (8) = 0

1 * 2^2 (4) = 4

0 * 2^1 (2) = 0

1 * 2^0 (1) = 1

Summing these products:

16 + 0 + 4 + 0 + 1 = 21

Therefore, the decimal representation of the binary number 10101 is 21.