Hex to Decimal

It is difficult to comprehend the magnitude of a base 16 number until it is presented in base 10; for instance, E0₁₆ is equal to 224₁₀. You must remember that usually fewer digits are necessary to represent a decimal value in base 16.

When you convert from base 16 to decimal, you may use the positional notation system for the powers of 16 (a bar graph). You can also convert the base 16 number to binary and then convert to base 10.

Note in the bar graph below that each power of 16 results in a tremendous increase in the decimal equivalent. Only one negative power (16^-1) is shown for demonstration purposes:

Just as you did with octal conversion, write out the hex number, placing each digit under the appropriate decimal value for that position. Multiply the decimal value by the base 16 digit and add the values. (Convert A through F to their decimal equivalent before multiplying). Let's take a look at an example.

Convert 2C₁₆ to decimal:

The decimal equivalent of 2C₁₆ is 44₁₀.

Use the same procedure we used with binary and octal to convert base 16 fractions to decimal.

If you choose to convert the hex number to binary and then to decimal, the solution will look like this:

Convert these base 16 numbers to base 10:

Q103. 24₁₆.
Q104. A5₁₆.
Q105. DB₁₆.
Q106. 3E6.5₁₆.