What is the process of converting a binary number to decimal?

The process of converting a binary number to decimal involves multiplying each digit by 2 raised to its positional value and summing the results.

To convert a binary number to a decimal number, you start from the rightmost digit (also known as the least significant bit) and move to the left, multiplying each digit by 2 raised to the power of its position, starting from zero. The sum of these products gives you the decimal equivalent of the binary number.

Let's take an example. Suppose we have the binary number 1011. Starting from the rightmost digit, we have:

- 1 (binary digit) x 2^0 (position value) = 1
- 1 (binary digit) x 2^1 (position value) = 2
- 0 (binary digit) x 2^2 (position value) = 0
- 1 (binary digit) x 2^3 (position value) = 8

Adding these products together, we get 1 + 2 + 0 + 8 = 11. So, the decimal equivalent of the binary number 1011 is 11.

This method works for any binary number, no matter how large. The key is to remember that each digit in a binary number represents a power of 2, starting from 2^0 on the right and increasing by one power as you move to the left. This is why binary numbers are also known as base-2 numbers: each digit is a multiple of a power of 2.

It's also worth noting that this process is the reverse of converting a decimal number to binary. When converting from decimal to binary, you divide the decimal number by 2 and record the remainder until you reach 0. The binary equivalent is the string of remainders read in reverse order. So, understanding how to convert between binary and decimal can help you better understand the relationship between these two number systems.