Binary to Decimal

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

1. Write the Binary Number: Start with the given binary number.
2. Assign Powers of 2: Assign powers of 2 to each digit from right to left, starting with 2^0 for the rightmost digit.
3. 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.