Numbering Systems

To my grandson Dylan, numbers, as I’ve been taught.

Question? Why am I blogging this. Hmmm, because it’s easier to send the link then the Text, and Superscripts and Subscripts, although I’m only using Superscripts here.

At one time, I thought a number like 486 was simply a number. But after going to school for Electronics, I learned something I never knew, because of the way we learned Binary used by Computers and Digital Devices Collectively.

There are several systems of numbers. Decimal is Base 10. Octal is Base 8, Binary is Base 2, and drum roll please, Hexadecimal is Base 16.

Oh, that Binary Thing, it was chosen because it’s on or off for representing numbers. It’s easy for Electronics to do. Just simple switching inside electronic chips can be used.

The number that denotes the Base is never used as a single number in its own system.

Base 10 is 0-9 which is 10 places.

Base 8 is 0-7 for 8 places.

Base 2 is 0-1, for 2 places.

Hexadecimal is Base 16 with 0 through 15, but the numbers 10, 11, 12, 13, 14, and 15 are represented in Hexadecimal as A, B, C, D, E, and F so technically Hexadecimal uses 0 thru F.

For the following, and in Math, it’s assumed that a number taken to the Zero Power is One.

486 is in reality 4×102+ 8×101+ 6×100
Or: 4x(10×10) + 8x(10) + 6x(1) Remember a number to the Zero Power is 1.

400+80+6 = 486

Sounds stupid, doesn’t it. But it’s how it works. Lets see a Binary Example.

Binary Number 1011

1×23 + 0x22 + 1×21 + 1×20

1x(2x2x2) + 0x(2×2) + 1x(2) + 1x(1)

1×8 + 0x4 + 1×2 + 1×1 = 11 in Decimal Numbers.

You can confirm it here: Binary to Decimal Conversion

The above link also talks about what I’ve demonstrated here.

Decimal 11 is Hexadecimal B and Binary 1011, what about Octal?

Octal is 0 thru 7, then:

Octal 10 for Decimal 8, Octal 11 for Decimal 9, Octal 12 for Decimal 10, and Octal 13 for Decimal 11.

Let’s prove it.

Octal is Base 8, the Base Number doesn’t appear in the system as a single digit, or 8 isn’t in Octal at all, and any number to the Zero power is one.

Octal 13 is 1×81 + 3×80

Or 1×8 + 3×1 = Decimal 11

Spooky huh?

Author: Dr-Artaud

A Doctor that is not a Doctor, but named after a character in the movie "No Such Thing", as is the Avatar.

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