Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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Ricky
2006-02-14 07:24:02

its not about transistors, its about charge in magnetic tape, there millions of seperate magnetic bits on a tape and the point either north or south, north being 0 south being 1. And its read by the computer.

You are talking about rom.  The first computers didn't even have rom, all they had was ram, which was not in the form of magnetic tape.

ryos
2006-02-14 05:50:56

Oh yeah, and then we'd need a calculator to count to 10. Natural logs would be a breeze, though!

MathsIsFun
2006-02-13 22:40:49

Every odd power ends up negative ... !  So 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6 = -2 + 4 -32 + 64 = 34

I have this idea in the back of my head that there might be a more "natural" number system than base10. Maybe we should have base "e"?

Zmurf
2006-02-13 20:12:40

wots the difference between base 2 and base -2, bar the 1*(02)^1 its identical because 1*(-2)^2 = 4 just like 1*(2)^2, is there sumthin' im missing?

MathsIsFun
2006-02-13 19:28:06

#### Ricky wrote:

But by far, the coolest base is -2:

0110 0110: 34 or 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6

Genius! I never thought of a negative base.

Does it have any wonderful uses (apart from confounding humans)?

MathsIsFun
2006-02-13 19:25:33

#### siva.eas wrote:

What is the total number of number systems that have been established today not counting decimal, binary, octal and hexadecimal number system?

Imperial: 12 inches in a foot, 3 feet in a yard, 6 feet in a fathom, 660 feet in a furlong, 5280 feet in a mile (6080 in a nautical mile), not to mention pints, gallons, quarts, pecks, bushels, roods, poles, perches et al.

And old British money required great arithmetic skill: 12 pennies in a shilling, 20 shillings in a pound. And a guinea was 1 pound and one shilling, wasn't it? Clerks, shopkeepers and accountants had to deal with this without thinking.

So ... lots!

Zmurf
2006-02-13 19:09:43

#### Ricky wrote:

(Whoever thought up binary and applied it to computers was a genius...)

It came naturally because transistors only have two states.

But by far, the coolest base is -2:

0110 0110: 34 or 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6

its not about transistors, its about charge in magnetic tape, there millions of seperate magnetic bits on a tape and the point either north or south, north being 0 south being 1. And its read by the computer.

Ricky
2006-02-09 09:49:52

Clocks use base 10...

mathsyperson
2006-02-09 09:35:33

#### ryos wrote:

The Babylonians used a base-60 number system. Yikes...how did they get anywhere with base 60?

Clocks seem to cope well enough.

Ricky
2006-02-08 12:35:01

(Whoever thought up binary and applied it to computers was a genius...)

It came naturally because transistors only have two states.

But by far, the coolest base is -2:

0110 0110: 34 or 1*(-2)^1 + 1*(-2)^2 + 1*(-2)^5 + 1*(-2)^6

ryos
2006-02-08 12:25:03

If you're just talking about bases, you can base a number system on any arbitrary base you want. It just depends on what's convenient for you. Computers use base-2 not because it's awesome, but because they don't have much of a choice considering they only have two states. (Whoever thought up binary and applied it to computers was a genius...)

The Babylonians used a base-60 number system. Yikes...how did they get anywhere with base 60?

siva.eas
2006-02-08 10:18:17

I have two questions.

What is the total number of number systems that have been established today not counting decimal, binary, octal and hexadecimal number system?

And what are they?