Octal Number System
The number with base eight is called octal number. It is represented by Q or O. We can generate these numbers with the combination of 0, 1, 2 3, 4, 5, 6, 7. We can represent these numbers wit suffix eight. Eg (5432)_{8}
Weighted value
85  84  83  82  81  80 
32768  4096  512  64  8  1 
Conversions from Decimal to Octal
Decimal number is repetitively divided by eight and remainders are arranged in the form of octal numbers.
Example
Convert (240)_{10}into octal.
8  240  0 
8  30  6 
3 
(240)_{10}= (360)_{8}
Convert (356)_{10}into octal.
8  356  4 
8  44  4 
4 
(365)_{10}=(444)_{8}
Conversions from Octal to Decimal.
Each octal is multiplied by its weighted position. The sum of all products is known as decimal form of octal.
Example
Convert the octal numbers into decimal
 (340)_{8}= 3 x 8^{2}+ 4 x 8^{1}+ 0 x 8^{0}=192 + 32 + 0 = (224)_{10}
 (175)_{8}= 1 x8^{2}+7 x 8^{1}+ 5 x8^{0}= (125)_{10}
Octal to Binary and Binary to Octal Conversions
The three digit format of binary digits is used for octal to binary conversions or vice versa.
Octal to Binary
3bits binary numbers are written for each octal digit.
Example
Convert (56)_{8} (octal) into binary.
Algorithm:
 Convert each octal digit into binary and make three digits grouping.
5= 101
6= 110
Now our equivalent binary number is (56)_{8}=(101110)_{2}
Convert (64102)_{8} into Binary number.
6= 110
4= 100
1= 001
0= 000
2= 010
Now our equivalent binary number is (64102)_{8}= (110100001000010)_{2}
Binary to Octal
The binary numbers are broken into 3bits section from last bit and convert into octal equivalent of each binary section. Table shows the decimal, octal and equivalent binary bits.
Decimal  Octal  Binary 
0  0  000 
1  1  001 
2  2  010 
3  3  011 
4  4  100 
5  5  101 
6  6  110 
7  7  111 
Example
Convert (10011)_{2} into octal number.
Algorithm
 make 3bits grouping from last bit.
010 011  convert each group into decimal numbers.
010 = 2
011 = 3
= (23)_{8}
Convert (1011010011)_{2} into octal number.
001 011 010 011
001= 1
011= 3
010= 2
011= 3
= (1323)_{8}
Octal to Hexadecimal
Algorithm
 Convert octal into binary.
 make groups of 4bits from last bit.
 convert each group into decimal numbers.
Example
1. (34765)_{8}into Hexadecimal number.
 Convert into binary
3= 011, 4= 100, 7=111, 6= 110, 5=101
(011100111110101)_{2}  Make a four digits group from the last bit of the binary number.
0011 1001 1111 0101 (Add 0 before the group to make four digit)
3 9 15 5 (Convert into equivalent decimal numbers)
=(39F5)_{16}Where F= 15
 The number with base eight is called octal number. It is represented by Q or O.
 When decimal number is repetitively divided by eight and remainders are arranged in the form of octal numbers,then decimal number are converted into octal.
 Each octal is multiplied by its weighted position. The sum of all products is known as decimal form of octal.
 The three digit format of binary digits is used for octal to binary conversions or vice versa.

The number with base eight is called _________.
octal number
hexa decimal number
binary number
decimal number

What is the octal value of the binary number 101110?
78
55
45
56

What is the octal value of the binary number 1011010011?
1133
1323
1324
1345

What is the binary value of the octal number 64?
110100
10101
110101
110111

What is the binary value of the octal number 63?
110011
110101
110111
10101

What is the hexadecimal value of the octal number 34765?
34F8
57B9
39B6
39F5

The base of octal number system is _________.
16
2
8
10

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GAuravNot understood the process 
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