Converting a binary number (a number expressed in base 2) to a decimal (base 10) is a straightforward process. The basic concept is to take the binary number and multiply each digit (also known as a “bit”) by the corresponding power of 2, and then add up all of the results.
Here’s an example of how to convert the binary number “1101” (which is equivalent to the decimal number 13) to decimal:
- Start with the rightmost digit (in this case, “1”). Multiply it by 2^0 (which is 1). The result is 1.
- Move to the next digit to the left (in this case, “0”). Multiply it by 2^1 (which is 2). The result is 0.
- Move to the next digit to the left (in this case, “1”). Multiply it by 2^2 (which is 4). The result is 4.
- Move to the next digit to the left (in this case, “1”). Multiply it by 2^3 (which is 8). The result is 8.
- Add up the results from step 1 to step 4. 1 + 0 + 4 + 8 = 13.
So the binary number “1101” is equivalent to the decimal number 13.
Another way to convert binary to decimal is by using the built-in functions of programming languages like python, for example, you can use int(“1101”,2) to get the decimal representation of the binary number “1101”
In general, to convert a binary number to decimal, you can use the following formula: Decimal = (b_n * 2^n) + (b_(n-1) * 2^(n-1)) + … + (b_1 * 2^1) + (b_0 * 2^0)
where b_n is the nth digit of the binary number (0 or 1) and n is the position of the digit, counting from the right (0 being the rightmost digit)