#🔒 bitwise XOR

37 messages · Page 1 of 1 (latest)

vagrant cosmos
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for given a and b
a^x +b^x has to be minimum for any given x.
there has to some property of XOR that will be used here

visual heartBOT
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@vagrant cosmos

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mint niche
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can you elaborate on what you actually need help with?

vagrant cosmos
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we are given a= 6 , b =12

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and an equation

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a^x + b^x

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it is asked for any given value of 'x' what will be the minimum answer for the equation

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i.e. a^x + b^x

mint niche
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is "+" an "or" in this case?

vagrant cosmos
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plus

mint niche
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okay, then what is the equation?

vagrant cosmos
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sum of two XOR operation

mint niche
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it's just a term, not an equation (equal sign is missing 😉 )

vagrant cosmos
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what will be the minimum value of the term a^x + b^x and for what x , if there are multiple value of x then wirte any of them

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0.0

rugged ferry
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Forget about the decimal number and just think in individual bits

vagrant cosmos
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sorry i dont copy

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for a = 6 and b=12 the minimum value occurs at x =4

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6^4 + 12^4 = 10

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apparently 10 is also 6^12

rugged ferry
vagrant cosmos
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aah

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answer for all cases is a^b , but don't understand how tho?

rugged ferry
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And look at the individual bits

0110
1100
^
?
```Both have to be `xor`'d by the same number (again think in bits). Say you look at the digit pointed to by `^`, what happens if `?` is 1/0? Does it matter here? When does it matter, and what do you do to minimize the sum of that digit then?
vagrant cosmos
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0110^0100 + 1100^0100

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ohh i think i got it

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so we have to neutral the second 1

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right?

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1100^0100 = 1000```
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since the third bit is the only one common

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right?

rugged ferry
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Well for each bit pair, there's basically only 3 cases: both are 1/0 or 1110, and there's a best bit to xor for each case
Then you can construct x bit by bit, or do some smart stuff and come up with a formula

vagrant cosmos
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ohh thankyou

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so for

1100^1100 = 0000```
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is this correct ? , 1100 is x

visual heartBOT
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