Binary to Decimal
Convert binary numbers to decimal effortlessly with our Binary to Decimal Converter. Translate binary sequences or codes into their decimal numerical representations quickly and accurately. Whether you're working with programming, data analysis, or digital systems, our tool simplifies the conversion process. Experience seamless binary-to-decimal conversions with our user-friendly Binary to Decimal Converter.
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.