Converting a binary number to a decimal number involves multiplying each digit in the binary number by the corresponding power of 2 and then summing up these products. Here are the steps to convert a binary number to a decimal number:
Write down the binary number.
Start from the right (the least significant bit) and assign a position value to each digit. The rightmost digit has a position value of 2^0 (which is 1), the next digit to the left has a position value of 2^1 (which is 2), the next digit to the left has a position value of 2^2 (which is 4), and so on, increasing the exponent by 1 as you move to the left.
Multiply each digit in the binary number by its corresponding position value and write down the result.
Sum up all the results from step 3 to get the decimal equivalent.
Here’s an example to illustrate the process:
Binary number: 1011
Step 2: Assign position values from right to left: 1st digit from the right: 2^0 = 1 2nd digit from the right: 2^1 = 2 3rd digit from the right: 2^2 = 4 4th digit from the right: 2^3 = 8
Step 3: Multiply each digit by its position value and write down the results: 1 * 1 = 1 0 * 2 = 0 1 * 4 = 4 1 * 8 = 8
Step 4: Sum up the results from step 3: 1 + 0 + 4 + 8 = 13
So, the binary number 1011 is equal to the decimal number 13.