Octal Number System
The number with base eight is called octal number. It is represented by Q or 8. This note explains octal number system and its conversions.
Summary
The number with base eight is called octal number. It is represented by Q or 8. This note explains octal number system and its conversions.
Things to Remember
- 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.
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Octal Number System
Octal
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
| 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
1. Convert (240)10into octal.
| 8 | 240 | 0 |
| 8 | 30 | 6 |
| 3 |
(240)10= (360)8
2. 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 82 + 4 x 81+ 0 x 80 =192 + 32 + 0 = (224)10
- (175)8= 1 x 82 +7 x 81+ 5 x 80 = (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
- (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
Lesson
Number System
Subject
Computer
Grade
Grade 9
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