Master the 'Positional Weight' multiplication method for converting binary, octal, or hexadecimal to decimal.
Hook about how positional values unlock the base-10 meaning.
Imagine receiving a coded message in a foreign language. To translate a binary, octal, or hexadecimal number back into a format we understand (decimal), you have to expand it using its positional weights.
The value of every digit in a number depends on its position. By mapping out these positions, you can decode any base system into base-10.
Visual calculation of 1101 binary to decimal.
Mapping binary digits to positional powers of 2 to find the decimal sum.
Explanation of applying this to base 8 and 16.
The beauty of the expansion algorithm is that it is universal. To convert base-8 or base-16 numbers to decimal, you simply swap the base multiplier to (Octal) or (Hexadecimal).
Convert 257 octal to decimal.
You are reading a low-level memory dump and come across an octal value that needs to be translated for a standard user interface. Following the expansion algorithm, convert the octal number into its decimal equivalent.