1.4 Hexadecimal Number Operation

Decimal basic concepts:

• Decimal is base 10.
• There are 10 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
• When you reach 10, you carry a “1” over to the next column
• The number after 9 is 10

Hexadecimal basic concepts:

• Hexadecimal is base 16.
• There are 16 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)
• When you reach 16, you carry a “1” over to the next column
• The number after F (decimal 15) is 10 in hex (or 16 in decimal)

Addition

Use the following steps to perform hexadecimal addition:
1. Add one column at a time.
2. Convert to decimal and add the numbers.
3a. If the result of step two is 16 or larger subtract the result from 16 and carry 1 to the next column.
3b. If the result of step two is less than 16, convert the number to hexadecimal.

Example:

AC5A9₁₆ + ED694₁₆

Step 1:

1. Add one column at a time

2. Convert to decimal & add (9 + 4 = 13)

3. Follow less than 16 rule

    Decimal 13 is hexadecimal D

Step 2:

1. Add next column

2. Convert to decimal & add (10 + 9 = 19)

3. Follow 16 or larger than 16 rule

    (19 – 16 = 3 carry a 1)


Step 3:

1. Add next column

2. Convert to decimal & add (1 + 5 + 6 = 12)

3. Follow less than 16 rule, convert to hex

    Decimal 12 is hexadecimal C



Step 4:

1. Add next column

2. Convert to decimal & add (12 + 13 = 25)

3. Follow 16 or larger than 16 rule

    (25 – 16 = 9 carry a 1)


Step 5:

1. Add next column

2. Convert and add (1 + 10 + 11 = 22)

3. Follow 16 or larger than 16 rule

    (22 – 16 = 6 carry a 1)



Step 6:

1. Add next column

2. Convert and add (1 + 0 + 0 = 1)

3. Follow less than 16 rule

Subtraction

It works pretty much the same with addition, the main difference is to borrow value from left digit for subtracting higher value numbers.

Example 1:

C675₁₆ - A247₁₆

When a borrow is required from the digit to the left, add 16 (decimal) to the current digit's value.

Example 2:

1C56F0₁₆ - FABD2₁₆

  1C56F0

-  FABD2

   CAB1E

Method:

1. 0 - 2, can't do so borrow 16 from next column, 16 - 2 =14 i.e. E
2. F (borrowed 1) so now E - D which is 14 - 13 = 1
3. 6 - B, can't do, so borrow 16 from next column, 22 (16+ 6) - 11 = 11, i.e. B
4. 5 (borrowed 1) so now 4 - A, can't do so borrow, 16 from next column, 20 (16+ 4) - 10 = 10 i.e. A
5. C (borrowed 1) so now B - F, can't do so borrow, 16 from next column, 27 (16+ 11) - 15 = 12 i.e. C