2. 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
3. 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)
4. Use the following steps to perform hexadecimal
addition:
1. Add one column at a time.
2. Convert to decimal and add the numbers.
3. If the result of step two is 16 or larger subtract the result
from 16 and carry 1 to the next column.
4. If the result of step two is less than 16, convert the
number to hexadecimal.
5. Example: (Use the color code in each step to see
what’s happening)
The problem:
You are to add these numbers:
A C 5 A 9
E D 6 9 4
Carry Over:
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
A C 5 A 9
E D 6 9 4
D
6. Carry Over: 1
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)
A C 5 A 9
E D 6 9 4
3 D
Carry Over: 1
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
A C 5 A 9
E D 6 9 4
C 3 D
7. Carry Over: 1
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)
A C 5 A 9
E D 6 9 4
9 C 3 D
Carry Over: 1
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)
A C 5 A 9
B D 6 9 4
6 9 C 3 D
8. Carry Over: 1
1. Add next column
2. Convert and add (1 + 0 + 0 = 1)
3. Follow less than 16 rule
0 A C 5 A 9
0 B D 6 9 4
1 6 9 C 3 D
F C B D 9
B A 5 0 4
Practice 1 C 3 A F
3 B 6 D F
1 A 0 8 A
D B C F 4
C C 9 A 9
F D 6 9 9
