Question

This is a shortcut to to convert base two to base ten, it is called the ____ ____ ____ where you can start at the left of the numeral and work your way to the right without first determining the place value of each bit.

Answer 1

The shortcut method for converting binary to decimal without determining the place value of each bit is known as the double dabble method. It involves a step-by-step process where you double the previous total and add the current digit, equivalent to how decimal place values shift with powers of ten.

Step-by-step explanation:

The process described refers to a method of converting binary numbers (base two) to decimal numbers (base ten), and it's called the double dabble method. This method allows you to start at the left of the numeral and work your way to the right without first determining the place value of each bit. It is a bit like using the powers of ten in the decimal system where you multiply or divide by powers of ten to shift the decimal place accordingly. However, in binary-to-decimal conversion, you're effectively doubling (since binary is base two) and adding per place.

For example, given the binary number 1101, you would start with the leftmost digit and 'double' the previous total and then 'add' the current digit:

• 1 (initialize)
• 2 (double 1) + 1 (add current digit) = 3
• 6 (double 3) + 0 (add current digit) = 6
• 12 (double 6) + 1 (add current digit) = 13

Thus, the binary number 1101 converts to the decimal number 13. This technique simplifies the conversion process and does not require the understanding or calculation of powers as in regular conversion maths.