Octal

Base-8 numeral system / From Wikipedia, the free encyclopedia

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The octal, or oct for short, is the base-8 positional numeral system, and uses the digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, uses a base-10 number system, hence a true octal system might use different vocabulary.

Numeral systems, bits and Gray code
hexdecoct3210step
0hex00dec00oct0000g0
1hex01dec01oct0001h1
2hex02dec02oct0010j3
3hex03dec03oct0011i2
4hex04dec04oct0100n7
5hex05dec05oct0101m6
6hex06dec06oct0110k4
7hex07dec07oct0111l5
8hex08dec10oct1000vF
9hex09dec11oct1001uE
Ahex10dec12oct1010sC
Bhex11dec13oct1011tD
Chex12dec14oct1100o8
Dhex13dec15oct1101p9
Ehex14dec16oct1110rB
Fhex15dec17oct1111qA

In the decimal system, each place is a power of ten. For example:

In the octal system, each place is a power of eight. For example:

By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to in decimal.

Octal numerals can be easily converted from binary representations (similar to a quaternary numeral system) by grouping consecutive binary digits into groups of three (starting from the right, for integers). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding to the octal digits 1 1 2, yielding the octal representation 112.

Table info: ...
The octal multiplication table
×123456710
1123456710
22461012141620
336111417222530
4410142024303440
5512172431364350
6614223036445260
7716253443526170
1010203040506070100
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