a problem can't understand it

**mido22** · August 7th 2010, 06:50 AM

here is the link of the problem but i can't understand the form of numbers
https://www.spoj.pl/problems/EASYPROB/

**undefined** · August 7th 2010, 07:17 AM

Originally Posted by mido22

here is the link of the problem but i can't understand the form of numbers
https://www.spoj.pl/problems/EASYPROB/

It's a combination of brain teaser and knowing something about binary.

137 is related to the string "2(2(2)+2+2(0))+2(2+2(0))+2(0)" in that $137=2^{2^2+2^1+2^0}+2^{2^1+2^0}+2^0$ . The binary representation of 137 is 10001001. See it?

**mido22** · August 7th 2010, 07:40 AM

i know about the binary and i understand the

but what is the relation betn. the binary of 137 and this form

**mido22** · August 7th 2010, 07:44 AM

do u meant that in this binary no.

10001001
the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

and second term (100) -> the power will be two terms as zeros 2^1+2^0

and so on

but here for example
73=2(2(2)+2) +2(2+2(0)) +2(0)
the binary of 73 = 100 100 1
this binary won't help me as i understand

**undefined** · August 7th 2010, 07:59 AM

Originally Posted by mido22

i know about the binary and i understand the

but what is the relation betn. the binary of 137 and this form

Originally Posted by mido22

do u meant that in this binary no.

10001001
the first term (1000) -> the power will be three terms as zeros 2^2+2^1+2^0

and second term (100) -> the power will be two terms as zeros 2^1+2^0

and so on

but here for example
73=2(2(2)+2) +2(2+2(0)) +2(0)
the binary of 73 = 100 100 1
this binary won't help me as i understand

I am a bit free with my notation in order to write compactly, I think it is legible

$73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0$

**mido22** · August 7th 2010, 08:10 AM

Originally Posted by undefined

I am a bit free with my notation in order to write compactly, I think it is legible

$73_{10} = 1001001_2 = 2^6 + 2^3 + 2^0 = 2^{110_2} + 2^{11_2} + 2^0 = 2^{2^2+2^1} + 2^{2^1+2^0} + 2^0$

i still understanding all except
how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
if i'mnot silly plz till me what usage of binary here

**mido22** · August 7th 2010, 08:15 AM

to understand what i want
i understood the image u put and
binary of 6 -> 110 and so on for powers

but how can u get the powers 6,3,0

**undefined** · August 7th 2010, 08:18 AM

Originally Posted by mido22

i still understanding all except
how can u get that the power of first term is 6 and second is 3 and third is 0 from the binary
if i'mnot silly plz till me what usage of binary here

So in decimal we have for example $12345 = 5\cdot10^0 + 4\cdot10^1 + 3\cdot10^2 + 2\cdot10^3 + 1\cdot10^4$ . More symbolically, write an n-digit decimal number as $a_{n-1}a_{n-2}\dots a_1a_0$ , then it is equal to $\displaystyle \sum_{k=0}^{n-1} a_k\cdot10^k$ .

It is the same in binary, just replace the 10 with 2.

**mido22** · August 7th 2010, 08:22 AM

i begin to understand u thx very much

**undefined** · August 7th 2010, 08:25 AM

Originally Posted by mido22

to understand what i want
i understood the image u put and
binary of 6 -> 110 and so on for powers

but how can u get the powers 6,3,0

Originally Posted by mido22

i begin to understand u thx very much

If it's still not clear, see attached image

**mido22** · August 7th 2010, 08:27 AM

Originally Posted by undefined

If it's still not clear, see attached image

nw it is very very clear thx very much

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