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)10into octal.

8 240 0
8 30 6
3

(240)10= (360)8

Convert (356)10into 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

  1. (340)8= 3 x 82+ 4 x 81+ 0 x 80=192 + 32 + 0 = (224)10
  2. (175)8= 1 x82+7 x 81+ 5 x80= (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

3-bits 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 3-bits 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 3-bits 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 4-bits from last bit.
  • convert each group into decimal numbers.

Example

1. (34765)8into 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)16Where 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.
0%
  • 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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