How to convert an octal value ?

How to convert an octal value ?

in different fields of human activity use different number systems.In everyday life we ​​use a decimal score, machine operations are carried out within the computer as binary and hexadecimal sequence operator sees when viewing the contents of a computer's memory.Therefore, we must learn how to quickly translate numbers into binary, octal, decimal and hexadecimal systems.

octal

Octal system is notable in that its base - eight - a power of two.This makes it possible to transfer in the octal system of binary and vice versa using mathematical tricks.Since the eight - two in the third degree, one digit octal system will proceed strictly in three digits of binary.And transfer is possible, using the table:

08 0002
18 0012
28 0102
38 0112
48 1002
58 1012
68 1102
78 1112

example, the number 10010111010102 need to translate an octal value.

  • first divide it into triads - segments by three digits.

1001011101 0102

  • So how exactly three figures did not happen, add two zeros to the left.The number will not change.

001 001 011 101 0102

  • Now replace every segment of its octal analogue, referring to the table.

January 1 3 2 8

received number 11328.

Translation of the decimal system in octal

In this case, a simplified method will not work.Consider for example the number of 176 210, which must be converted into octal appearance.

  1. Divide with the remainder of 1762 to 8 turns 220 and 2 in the residue.220 more than 8, so we continue.
  2. Divide the residue with 220 turns 8. 27 and 4 in the residue.27 more than 8, so we continue.Divide
  3. residue with 8 to 27 turns 3 and 3 in the residue.3 is less than 8, division is completed.

Now you need to write down first, the last remnant of, and then in the reverse order of the partial division at all stages.

Last remainder is 3. Private 3 stage is 3. Private 2 stage is 4. Private 1 point is equal to 2. The resulting number 33428, which is the correct answer.

How to transfer to the octal system of decimal simpler?First of decimal numbers must be converted into binary form, and then in octal by using the table.Conversion from decimal to binary completely identical to the described algorithm it is necessary not only to divide by eight and, respectively, by two.It is because to divide into two simpler than on eight of the transfer in decimal or hexadecimal systems in octal binary often use.And as sixteen - two in the fourth degree, to translate hex into binary system, there is the same table, but to segments of four digits.