Showing posts with label Octal Arithmetic. Show all posts
Showing posts with label Octal Arithmetic. Show all posts

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

Octal Multiplication Solved Examples

Octal Multiplication Solved Examples
This is my third article on octal number system arithmetic. In this article I am going to explain octal numbers multiplication. I will also discuss multiplication using octal multiplication table.There are my posts on octal addition and octal subtraction.

Key Questions:
  • How to perform multiplication in octal number system?
  • How to perform fractional octal numbers multiplication?
  • Discuss octal multiplication table

Octal Number System Multiplication Table:



X
0
1
2
3
4
5
6
7
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
2
0
2
4
6
10
12
14
16
3
0
3
6
11
14
17
22
25
4
0
4
10
14
20
24
30
34
5
0
5
12
17
24
31
36
43
6
0
6
14
22
30
36
44
52
7
0
7
16
25
34
43
52
61

Octal Number System Multiplication Examples:

The multiplication process of octal numbers are same as other number systems. You can verify your result by using this  online converter.The points you should keep in mind while multiplying octal numbers:
  • If the sum exceeds 7 ( 0,1,2,3,4,5,6,7) you need to evaluate the equivalent octal value.
  • Divide the number by 8 and find its equivalent octal value. Quotient is going to be carry while remainder taken as sum

For example 5)8*6)8=30)10

   5
  *6
  36)8

   3  ← quotient as carry
8⟌30
      24
        6  ← remainder as sum
   


Example#01:777)8*33)8
           2  2   ←  carry
          7 7 7
           *33           
      1    1    1      ←  carry
       2 7 7 5
  2  7  7 5 X
  3  2  7 4 5


Decimal
Octal equivalent
Sum/remainder
Carry/quotient
7*3
21
21÷8=25
5
2
7*3
21+2
23÷8=27
7
2
7*3
21+2
23÷8=27
7
2
7+5
12
12÷8=14
4
1
7+7+1
15
15÷8=17
7
1
2+7+1
10
10÷8=12
2
1


Answer: 32745)8


Example#02:466.4)8*2.7)8
              1   1    1      
         5    5   3
        4 6 6 . 4
            *2 . 7
          1    
       4 1 7 5  4
  1  1  5 5  0 X
   1 5  7 4. 5  4


Decimal
Octal equivalent
Sum/remainder
Carry/quotient
7*4
28
28÷8=24
4
2
7*6
42+3
45÷8=5
5
5
7*6
42+5
47÷8=47
7
4
7*4
28+5
33÷8=41
1
4
2*4
8
8÷8=10
0
1
2*6
12+1
13÷8=15
5
1
2*6
12+1
13÷8=15
5
1
2*4
8+1
9÷8=11
1
1
7+5
12
12÷8=14
6
1

Answer:1574.54)8


Example#03:3636)8*741)8

Let's try to solve an example using octal multiplication table.

X=3636
Y=741
1*6 find the intersection of 3 and 6. Which is 6. Similarly for all the products refer table.
                 5  3   5
          3 1  3
          3 6 3 6
           *7 4 1
    1     1  
           3 6 3 6
    1 7 1 7 0 X
 3 2 5 2 2 X X
3 4  4 7 7 3 6

Answer: 3447736)8

Conclusion:
This is all about octal numbers multiplication. I verified and checked all the answers and solutions. If you still find any logical or typographical mistake, please inform me. If you find this post helpful, please like it. 

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