The document discusses conversion between decimal and octonary number systems. It provides examples of converting decimal numbers to their octonary equivalents and vice versa. It also discusses addition, subtraction, multiplication and division of octonary numbers. Examples are given for performing each operation in octonary. Key facts about octonary numbers like 8=10 and addition/multiplication tables are also presented.

1. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
CONVERSION FROM DECIMAL TO OCTONARY
Example -26 Decimal to Octonary
(422)10 = (646)8
CONVERSION FROM OCTONARY TO DECIMAL
Example -27 Octonary to Decimal
646 = 6 x 82
+ 4 x 81
+ 6 x 80
646 = 6 x 64 + 4 x 8 + 6 x 1
646 = 384 + 32 + 6
646 = 422
(646)8 = (422)10
8 422
8 52 6
6 4

2. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
Addition Facts in Octonary:
8 = 10
9 = 11
10 = 12
11 = 13 and so on
a) 4
+ 3
7 (no need to change base)
b) 5
+ 3
10 (5 + 3 = 8 in octa 8 is 10)
c) 5
+ 4
11 (5 + 4 = 9 in octa 9 is 11)
d) 6
+ 5
13 (6 + 5 = 11 in octa 11 is 13)
Example –28
5 7 + 3 2
Solution: 5 7 (7 + 2 = 9 in octal 9 is 11)
+ 3 2 (1 + 5 + 3 = 9 in octal 9 is 11)
1 1 1
Example- 29
1 0 6 7 + 6 3 4
Solution:
1 0 6 7
+ 6 3 4
1 7 2 3

3. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
SUBTRACTION FACTS IN OCTONARY
Example-30
1 1 1 – 5 7
Solution:
1 1 1 (in subtraction, we directly take 8 as carry
- 5 7 and add it in the existing digit).
3 2 Step 1) 8 + 1 = 9 and 9 – 7 = 2
Step 2) 8 + 0 = 8 and 8 – 5 = 3
Example-31
1 7 2 3 – 1 0 6 7
Solution:
1 7 2 3
-1 0 6 7
6 3 4
MULTIPLICATION FACTS IN OCTONARY
Example-32:
5 7 x 7
Solution:
57 (7 × 7 = 49 in octal 49 is 61)
x 7 (7 × 5 = 35 + carry = 35 + 6 = 41 in octal 41
5 1 1 is 51).
Example-33:
1 3 1 x 2 7 1
Solution:
1 3 1
x 2 7 1
1 3 1
1 1 5 7 x
2 6 2 x x
4 0 1 2 1

4. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
DIVISION FACTS IN OCTONARY
Example-34:
3 6 7 2 3 ÷ 7
Solution:
First to make table
7 x 1 = 7
7 x 2 = 1 6 (use multiplication method of base 8)
7 x 3 = 2 5 (use multiplication method of base 8)
7 x 4 = 3 4 (use multiplication method of base 8)
7 x 5 = 4 3 (use multiplication method of base 8)
7 x 6 = 5 2 (use multiplication method of base 8)
7 x 7 = 6 1 (use multiplication method of base 8)
4325
7 36723
- 34
x 2 7
2 5
x 2 2
1 6
x 4 3
x 4 3
x x x
3 6 7 2 3 = 4 3 2 5
7

5. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
Example-35:
1 3 3 5 6 5 ÷ 1 7
Solution:
First to make table
17 x 1 = 1 7
17 x 2 = 3 6 (use multiplication method of base 8)
17 x 3 = 5 5 (use multiplication method of base 8)
17 x 4 = 7 4 (use multiplication method of base 8)
17 x 5 = 1 1 3 (use multiplication method of base 8)
17 x 6 = 13 2 (use multiplication method of base 8)
17 x 7 = 1 5 1 (use multiplication method of base 8)
6073
17 133565
- 132
x 1 5 6
1 5 1
x 5 5
5 5
x x
1 3 3 5 6 5 = 6 0 7 3
17