Hexadecimal Addition Examples

Hexadecimal Addition Solved Examples


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)

Recommended Books

By - No comments:
Labels:

Octal Division Solved Examples

Octal Division Solved Examples

This is my fourth article on octal arithmetic. In this article I am going to solve some examples on octal division. This is very easy task and principles and rules of division remain same. Here are articles on octal number systems. These articles provide tutorials on mathematical operations on octal number systems which includes octal numbers addition,octal numbers subtraction and octal numbers multiplication.

Key Questions:
  • How to perform division in octal numbers system?
  • How to perform fractional octal numbers division

Division In Octal Number System (Solved Examples):

To solve division examples you must know how to perform multiplication on octal numbers. I will solve examples on each case. First case in which dividend and divisor both are integers. Second case in which dividend has an octal point and divisor is an integer. Third case in which both dividend and divisor both have floating point numbers. You can check your results by using this online converter.

Example#01:6573)8÷16)8
First we make a table for 16 and it's multiples.


Decimal
Octal
16*1
16
14
16*2
32
34
16*3
48
52
16*4
64
70
16*5
80
106
16*6
96
124


          366.4
16 ⟌6573
        52
        137
        124
          133
          124
              70
               70
               XX

Answer:366.4)8

Example#02:457.43)8÷7)8
First make a table for 7 and it's multiples



Decimal
Octal
7*1
7
7
7*2
14
16
7*3
21
25
7*4
28
34
7*5
35
43
7*6
42
52
7*7
49
61

       53.27
7 ⟌457.43
      43
        27
        25
          24
          16
             63
              61
              2

Answer:53.27)8

Example#03:737.72)8÷1.2)8
Shifting octal point makes the problem easy. According to mathematical rule shifting octal point of numerator upto one place then you have to shift octal point of denominator upto one place as well.

7377.2)8÷12)8

After shifting octal point divisor/denominator is free from octal point.

Let's make table for 12 and it's multiples.



Decimal
Octal
12*1
12
10
12*2
24
22
12*3
36
34
12*4
48
50
12*5
60
62
12*6
72
74
12*7
84
106


         577.73
12 ⟌7377.2
        62
        117
        106
          117
          106
             112
             106
                40
                36
                  2
        
Answer:577.73)8

By - 13 comments:
Labels:
Subscribe to: Comments (Atom)

Popular Posts