HexadecimalAddition
Decimalbasic concepts:
Decimalis base 10.
Thereare 10 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Whenyou reach 10, you carry a “1” over to the next column
Thenumber after 9 is 10
Hexadecimalbasic concepts:
Hexadecimalis base 16.
Thereare 16 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D,E, F)
Whenyou reach 16, you carry a “1” over to the next column
Thenumber after F (decimal 15) is 10 in hex (or 16 in decimal)
Use thefollowing steps to perform hexadecimal addition:
1. Addone column at a time.
2. Convertto decimal and add the numbers.
3a. If the result of step two is 16 orlarger subtract the result from 16 and carry 1 to the next column.
3b. If the result of step two is lessthan 16, convert the number to hexadecimal.
Example: (Use the color code ineach step to see what’s happening)
The problem:
 
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

*********************************************************************************
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

*********************************************************************************
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

*********************************************************************************
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

For substraction
http://www.wisconline.com/objects/ViewObject.aspx?ID=TMH3703
complement the substraction portion and do normal addition as explained above
569D
 FDA
569D
 0FDA
Now find complement of 0FDA = convert every bit to dec and 16val.
So, 0FDA becomes F025
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