What is the mathematical operation to convert a binary to decimal?

To convert a binary number to decimal, the process involves taking each digit of the binary number and multiplying it by 2 raised to the power of its position, counting from right to left, starting at zero. This means that each digit is valued not just by its face value but by its place value in terms of powers of 2.

For example, in the binary number 1011, the rightmost digit is in the 0th position, the next is in the 1st position, the next in the 2nd position, and so forth. The conversion is performed as follows:

• The rightmost '1' corresponds to (2^0) (which equals 1).

• The next digit '1' corresponds to (2^1) (which equals 2).

• The '0' corresponds to (2^2) (which equals 0, as any number times zero is zero).

• The leftmost '1' corresponds to (2^3) (which equals 8).

Adding these values together (1 + 2 + 0 + 8) gives the decimal equivalent of 11.

Thus, the mathematical operation that describes this process succinctly is the summation