- #1

gabe

- 4

- 0

what is 2+2?

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- Thread starter gabe
- Start date

- #1

gabe

- 4

- 0

what is 2+2?

- #2

ceptimus

- 299

- 1

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

- #3

TenaliRaman

- 644

- 1

G = {Z,+,*}

2 e Z

2+2 e Z

:p

2 e Z

2+2 e Z

:p

- #4

The Bob

- 1,119

- 0

ceptimus said:

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

Base?

The Bob (2004 ©)

- #5

The Bob

- 1,119

- 0

My Answer: 2+2

The Bob (2004 ©)

- #6

Ian Rumsey

- 31

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The ? may indicate another digit, so it could read 2+21 or 2+22 etc, etc

- #7

gabe

- 4

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man your stupid, 2+2=4 even a 5 year old would know that

- #8

K.J.Healey

- 622

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then its not really an expert puzzle now is it?

- #9

Gokul43201

Staff Emeritus

Science Advisor

Gold Member

- 7,176

- 22

gabe said:man your stupid, 2+2=4 even a 5 year old would know that

And you must be about 7 years old, because even an eight-year-old will know that the correct word to be used in your punctuation challenged "sentence" - the only puctuation used is the wrong one and you really should have three sentences there - is "you're", not "your" !

<Just a note that I'm aware of the 'conjunction rule' which is really archaic - in case you were planning on bringing that up.>

- #10

Good one, Goku. You say what I think.

- #11

The Bob

- 1,119

- 0

So what was the point in posting it gabe if you didn't want an unusual answer?

The Bob (2004 ©)

The Bob (2004 ©)

- #12

gabe said:man your stupid, 2+2=4 even a 5 year old would know that

lol... trollism at its finest.

- #13

gabe

- 4

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it was a joke! man that was funny :rofl:

- #14

ceptimus

- 299

- 1

The Bob said:Base?

The Bob (2004 ©)

All your base are belong to us.

- #15

The Bob

- 1,119

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ceptimus said:All your base are belong to us.

Not getting it at all.

In Confusion

The Bob (2004 ©)

- #16

TenaliRaman

- 644

- 1

1*10^2 + 2*10 + 3

This representation as we know it is called the decimal representation.

Also this is called the *base 10* representation

cuz the number is written in the powers of 10.

In general a base 10 number can be written as,

a_n*10^n + ...+a_1*10+a_0

where 0<= a_i <=9 for all 0<=i<=n

As we can have base 10 representaion then we can have any base 'r' representation ...

A base r number can be represented as,

a_n*r^n + ...+a_1*r+a_0

where 0<= a_i <=r-1 for all 0<=i<=n

e.g "5 in base 10" is "101 in base 2"

note that : 1*2^2 + 0*2 + 1 = 5

Hope this helps.

-- AI

- #17

The Bob

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TenaliRaman said:e.g "5 in base 10" is "101 in base 2"

note that : 1*2^2 + 0*2 + 1 = 5

I think it will help and has but could you please write out the bases, above, and their equations, like at the top of your post.

So 5 in base 10 = 5

101 in base 2 = 5 because 1*2^1 + 0 + 1?

Sorry I am a pain but I have little understanding of this.

Thanks

The Bob (2004 ©)

- #18

ceptimus

- 299

- 1

In (say) base 4, we only have four symbols: 0,1,2,3

so counting in base 4 looks like this: 0,1,2,3,10,11,12,13,20,21,22,23,30...

The 'ultimate' low base is base 2 where only two symbols are used: 0,1

This base is used by computers as the 0 and 1 can be easily represented by the absence or presence of a voltage, or current, or charge etc. Because it is so widely used, Base 2 has a special name: Binary.

Counting in Base 2 (aka Binary) looks like this: 0,1,10,11,100,101,110,111,1000...

Hope that helps.

'All of your base are belong to us' is a cult-saying on the internet. It came from a video game. Try googling on it to find more, if you're interested.

- #19

The Bob

- 1,119

- 0

Sorry guys, I took ages to get that.

Thanks TenaliRaman and Ceptimus. Appreciate the help.

The Bob (2004 ©)

- #20

check

- 144

- 0

0,00,000,0000 etc

or no zero and do 1,11,111,1111 ?

- #21

The Bob

- 1,119

- 0

ceptimus said:The 'ultimate' low base is base 2 where only two symbols are used: 0,1

check said:In base 1

No base 1. Don't know why but not base 1.

The Bob (2004 ©)

- #22

nucleartear

- 27

- 0

May be the fingers are an excellent example of base 1!

- #23

TenaliRaman

- 644

- 1

ppl have come up with many different representations which is in close analogy with this base representation

If u consider 0,1,2,3,4,5,6,... as just weighted symbols and that any base r representation as a representation which uses no more than abs(r) different symbols, then one can come up with many representations (Ofcourse all these representations need not have a bijection with the natural numbers).

So in view of this,

we can sort of have a base 1 representation, the counting in this schema would be

a,aa,aaa,aaaa,aaaaa,...

(One can use any symbol instead of a and assign it the weight 1)

This is called as a unary representation. (This is highly useful in many analysis of Turing machines)

One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).

A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.

e.g,

1 = 1

0 = 0

11 = -1

10 = -2

100 = 4

101 = 5

110 = 2

and so on...

-- AI

- #24

The Bob

- 1,119

- 0

TenaliRaman said:One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).

A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.

e.g,

1 = 1

0 = 0

11 = -1

10 = -2

100 = 4

101 = 5

110 = 2

and so on...

-- AI

Erm... :uhh: am I the only one that doesn't understand this?

Sorry AI but I don't get it. Being slow again.

The Bob (2004 ©)

- #25

4newton

- 191

- 0

If you are a mathematician you answer is 4

If you are an experimental physicist you will need to measure it.

If you are a theoretical physicist you will dream up some relative number.

If you are an account you will ask what do you want it to be.

- #26

TenaliRaman

- 644

- 1

haven't got much time now ...

see if this helps,

abs(-2) = 2

so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,

1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

- #27

The Bob

- 1,119

- 0

TenaliRaman said:

haven't got much time now ...

see if this helps,

abs(-2) = 2

so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,

1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

I believe I understand but I will have to do some in my own time and post again.

Cheers for the help :thumbs_up

The Bob (2004 ©)

- #28

Learning Curve

- 116

- 0

... binary code is in a base 2; 01,010,

Base is the number of digits one number place can hold.

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