This is my first article on hexadecimal arithmetic. In this article I am going to explain how to add numbers in hexadecimal or base 16 number system?
Key Questions:
- How to perform addition on hexadecimal or base 16 number system?
- How to perform fractional hexadecimal numbers addition?
Hexadecimal Addition Table:
+
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
0
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
1
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
2
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
3
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
4
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
5
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
6
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
7
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
8
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
9
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
A
|
A
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
B
|
B
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
1A
|
C
|
C
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
1A
|
1B
|
D
|
D
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
1A
|
1B
|
1C
|
E
|
E
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
1A
|
1B
|
1C
|
1D
|
F
|
F
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
1A
|
1B
|
1C
|
1D
|
1E
|
- The first row is X
- The first column is Y
- The rest of table is Sum
- For example 4+9 = D. X=4, Y=9, locate X and Y. The intersection of X and Y is the sum
Hexadecimal Addition Examples:
The addition of hexadecimal numbers are same as addition in other number systems. The points you should keep in mind are:
- If sum of a column exceeds F)16 add them as decimal numbers. Then you have to evaluate its equivalent hexadecimal value
- To evaluate equivalent hexadecimal number divide it by 16. The remainder is going to be sum and quotient is going to be carry
Hexadecimal
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
Decimal
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
Example#01:9A)16+4B)16
1
9 A
+4 B
E 5
1 ← quotient as carry
16⟌21
16
5 ← remainder as sum
Decimal
|
Hexadecimal
|
Sum/remainder
|
Carry/quotient
| |
A+B
|
10+11
|
21÷16
|
5
|
1
|
1+9+4
|
14
|
E
|
If you use addition table it is easy to solve.
Answer: E5)16
Example#02:AF.C1)16+78.989)16
1 1
A F . C 1 0
+7 8 . 9 8 9
1 2 8 . 5 9 9
Decimal
|
Hexadecimal
|
Sum/remainder
|
Carry/quotient
| |
C+9
|
12+9
|
21÷16
|
5
|
1
|
1+F+8
|
24
|
24÷16
|
8
|
1
|
1+A+7
|
1+10+7
|
18÷16
|
2
|
1
|
Answer:128.599)16
Solve With the Help of Addition Table:
Example#01:67.B)16+94.F)16
1
6 7 . B
+9 4 . F
F C . A
Find X=B and Y= F in the table.
F+B=1A
X=7+1=8 and Y= 4 look in the table
8+4=C
X=6 and Y=9 look in the table
6+9=F
Answer:FC.A)
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