Hexadecimal Arithmetic

Hexadecimal Number System

Following are the characteristics of a hexadecimal number system.

Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
Also called base 16 number system.
Each position in a hexadecimal number represents a 0 power of the base (16). Example − 16⁰
Last position in a hexadecimal number represents an x power of the base (16). Example − 16^x where x represents the last position - 1.

Example

Hexadecimal Number − 19FDE₁₆

Calculating Decimal Equivalent −

Step	Hexadecimal Number	Decimal Number
Step 1	19FDE₁₆	((1 × 16⁴) + (9 × 16³) + (F × 16²) + (D × 16¹) + (E × 16⁰))₁₀
Step 2	19FDE₁₆	((1 × 16⁴) + (9 × 16³) + (15 × 16²) + (13 × 16¹) + (14 × 16⁰))₁₀
Step 3	19FDE₁₆	(65536 + 36864 + 3840 + 208 + 14)₁₀
Step 4	19FDE₁₆	106462₁₀

Note − 19FDE₁₆ is normally written as 19FDE.

Hexadecimal Addition

Following hexadecimal addition table will help you greatly to handle Hexadecimal addition.

To use this table, simply follow the directions used in this example − Add A₁₆ and 5₁₆. Locate A in the X column then locate the 5 in the Y column. The point in 'sum' area where these two columns intersect is the sum of two numbers.

A₁₆ + 5₁₆ = F₁₆.

Example − Addition

Hexadecimal Subtraction

The subtraction of hexadecimal numbers follow the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10₁₀. In the binary system, you borrow a group of 2₁₀. In the hexadecimal system you borrow a group of 16₁₀.

Example - Subtraction