In decimal systems each decimal place is a base of 10. For example:
In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number system based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult and instead proposed 8 as base. In 1718 Swedenborg wrote a manuscript, which has not been published: "En ny rekenkonst som om vexlas wid Thalet 8 i stelle then wanliga wid Thalet 10" ("A new arithmetic (or art of counting) which changes at the Number 8 instead of the usual at the Number 10"). The numbers 1-7 are there denoted by the consonants l, s, n, m, t, f, u (v) and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule.
At the time when octal originally became widely used in computing, systems such as the IBM mainframes employed 24-bit (or 36-bit) words. Octal was an ideal abbreviation of binary for these machines because eight (or twelve) digits could concisely display an entire machine word (each octal digit covering three binary digits). It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the operator consoles; where binary displays were too complex to use, decimal displays needed complex hardware to convert radixes, and hexadecimal displays needed to display letters.
All modern computing platforms, however, use 16-, 32-, or 64-bit words, with eight bits making up a byte. On such systems three octal digits would be required, with the most significant octal digit inelegantly representing only two binary digits (and in a series the same octal digit would represent one binary digit from the next byte). Hence hexadecimal is more commonly used in programming languages today, since a hexadecimal digit covers four binary digits and all modern computing platforms have machine words that are evenly divisible by four. Some platforms with a power-of-two word size still have instruction subwords that are more easily understood if displayed in octal; this includes the PDP-11. The modern-day ubiquitous x86 architecture belongs to this category as well, but octal is almost never used on this platform.
The prefix or suffix customarily used to represent an octal number is "o" (i.e. o73), as binary and hexadecimal are represented by 'b' and 'h' or 'x' respectively, although 'q' is also seen as a way to make it more visually distinct from zero.
Previous methods can be combined to convert decimal numbers with integer and fractionary parts.
If you want to convert decima number to other number system as hexadecimal, octal, binary etc. You must divide the number by the number system you converting to. For example decimal to hexadecimal:610
3050/16 = 190 rem 10 190/16 = 11 rem 14 11/16 = 0 rem 11 asw: BEA
remember when you write your answer you start from bottom to the top.
Example: Convert octal 764 to decimal system. 764 (base 8) = 7 x 8² + 6 x 8¹ + 4 x 8° = 448 + 48 + 4 = 500 (base 10)
For double digit numbers this method amounts to taking the first number, multiplying it by 8 and then adding the second to get the total. Example: 65 in octal would be 53 in decimal (6*8 + 5 = 53)
For instance, conversion of binary 1010111100 to octal:
Thus 10101111002 = 12748
For instance, convert octal 1057 to hexadecimal:
Thus 10578 = 22F16
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