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.
A number system that uses eight different digits to represent different values is known as octal number system. The base of octal number system is 8 because it consist eight digits from 0 to 7. The octal number system is used in the computer to represent binary numbers. The place values in the octal number can be expressed by using powers of 8.
The procedure for conversion of octal numbers to their decimal equivalents is similar to conversion of binary numbers to their decimal equivalents but with the difference, that the base used in this case is 8 instead of 2 used in binary.
Solution:
3 2 1 0 (weight)
Octal Number: 5 2 6 4
Decimal Equivalent: 5×8^{3} + 2×8^{2} + 6×8^{1} + 4×8^{0}
= 5×512 + 2×64 + 6×8 + 4×1
= 2560 + 128 + 48 + 4
= 2740
Hence, (5264)_{8 }= (2740)_{10}
Octal digit is represented in 3 bits. An octal number is converted to its binary equivalent by just substituting the respective binary value for each digit of the octal number.
Binary Table
Octal  Binary 
0  000 
1  001 
2  010 
3  011 
4  100 
5  101 
6  110 
7  111 
Solution:
Octal Number: 3 2 0 6
Binary Equivalent: 11 010 000 110 (From Binary Table)
Hence, (3206)8 = (11010000110)_{2}
There is no any direct method to convert octal number into octal. So, at first the given octal number is converted into its binary equivalent then the result will be converted into hexadecimal as in previous methods.
Octal Number: 3 2 5 6
Binary Equivalent: 11 010 101 110 (From Binary Table)
Again,
Paired Hexadecimal
Equivalent (4 bits): 110 1010 1110 (pairing from rightmost digit)
Hexadecimal Equivalent: 6 A E (From Binary Table)
Hence, (3256)_{8} = (6AE)_{16}

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

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

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

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

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

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

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

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