Hexadecimal Addition

Addition can be done directly with hexadecimal numbers by remembering that the hexadecimal digits 0 through 9 are equivalent to decimal digits 0 through 9 and that hexadecimal digits

A through F are equivalent to decimal numbers 10 through 15. When adding two hexadecimal numbers, use the following rules. (Decimal numbers are indicated by a subscript 10.)

  1. In any given column of an addition problem, think of the two hexadecimal digits in terms of their decimal values. For instance, 5(16) = 5(10) and C(16) = 12(10). 
  2. If the sum of these two digits is 15(10) or less, bring down the corresponding hexadecimal digit.
  3. If the sum of these two digits is greater than 15(10), bring down the amount of the sum that exceeds 16(10) and carry a 1 to the next column.
EXAMPLE 1

Add the following hexadecimal numbers:



(a) 23(16) + 16(16)
(b) 58(16) + 22(16)
(c) 2B(16) + 84(16)
(d) DF(16) + AC(16)

Solution:





Hexadecimal Subtraction

As you have learned, the 2’s complement allows you to subtract by adding binary numbers. Since a hexadecimal number can be used to represent a binary number, it can also be used to represent the 2’s complement of a binary number.
There are three ways to get the 2’s complement of a hexadecimal number. Method 1 is the most common and easiest to use. Methods 2 and 3 are alternate methods

Method 1: Convert the hexadecimal number to binary. Take the 2’s complement of the binary number. Convert the result to hexadecimal. This is illustrated in Figure 2–4.

FIGURE 2–4 Getting the 2’s complement of a hexadecimal number, Method 1.

Method 2: Subtract the hexadecimal number from the maximum hexadecimal number and add 1. This is illustrated in Figure 2–5.

FIGURE 2–5 Getting the 2’s complement of a hexadecimal number, Method 2.

Method 3: Write the sequence of single hexadecimal digits. Write the sequence in reverse below the forward sequence. The 1’s complement of each hex digit is the digit directly below it. Add 1 to the resulting number to get the 2’s complement. This is illustrated in Figure 2–6.

FIGURE 2–6 Getting the 2’s complement of a hexadecimal number, Method 3.

EXAMPLE 2

 Subtract the following hexadecimal numbers:

(a) 84(16) - 2A(16) 

(b) C3(16) - 0B(16)

Solution: