Hexadecimal Calculation—Add, Subtract, Multiply, or Divide

Convert Hexadecimal Value to Decimal Value

Convert Decimal Value to Hexadecimal Value

The hexadecimal number system (hex) functions virtually identically to the decimal and binary systems. Instead of using a base of 10 or 2 respectively, it uses a base of 16. Hex uses 16 digits including 0-9, just as the decimal system does, but also us...

Hex Addition

Hex addition follows the same rules as decimal addition with the only difference being the added numerals A, B, C, D, E, and F. It may be convenient to have the decimal equivalent values of A through F handy when performing hex operations if the values have not yet been committed to memory. Below is an example of hex addition. Work through the example, and refer to the text below it for further details. Hex addition involves calculating basic decimal addition while converting between hex and decimal when values larger than 9 (the numerals A through F) are present. In the example above, B + 8 in decimal is 11 + 8 = 19. 19decimal is 13hex, since there is 1 set of 16, with 3 left over. Just like in decimal addition, the 1 carries over to the next column. Hence, the next column works out to be 1 + A (10) + 7 = 18decimal, or 12hex. Carry over the 1 to the final column resulting in 1 + 8 + B (11) = 20decimal, or 14hex. This yields the result of 1423hex.

Hex Subtraction

Hex subtraction can be computed much the same way as hex addition; by performing the operation while converting between hex and decimal values. The most significant difference between hex and decimal subtraction involves borrowing. When borrowing in he...

Hex Multiplication

Hex multiplication can be tricky because the conversions between hex and decimal when performing the operations require more effort since the numerals tend to be larger. Having a hexadecimal multiplication table can be helpful (one is provided below). Otherwise, manual conversion between decimal and hex will be necessary for each step. Below is an example of hex multiplication. To the right of the example, each of the multiplication and addition steps is shown. Note that all of the numerals used are hex. Refer to the addition section if necessary.

Hex Division

Long division in hex is identical to long division in decimal, except that the multiplication and subtraction occur in hex. It is also possible to convert to decimal and perform long division in decimal, then convert back once complete. For illustrative purposes, the division example will be calculated entirely in hex. As with multiplication, having a hexadecimal multiplication table (one is provided below) would be convenient while conducting hex division. Below is an example. Note that all numerals in the example are hex. Although no borrowing occurs in the example below, remember that borrowing in hex results in 16decimal being borrowed, rather than 10decimal. Refer to the hex subtraction section for further details.

Hexadecimal Multiplication Table