how to Reverse bitwise & operator

[David P]

Hi,

I'm new to bitwise operations.
Please help me to do this:

var str = "some string"
for each characters in str:
     past char & this char

this is ok, & i can do this. but, now i want to decode this to find original string. how can i do this? any idea?

thanks for your help.

[helios]

I don't think it's possible for AND, since it destroys information.
For example, x&0==0. Now there's no way to know what the value of x was, because it was completely overwritten with zeroes.

[David P]

dear Helios,

I have written this algorithm on the paper.
can you convert to c++ source code?

s(n) means the n'th character in original variable.
e(n) means the n'th character in encode variable.
note that binaries are the ASCII characters.

original variable:
10011101 -> s(1)
10001011 -> s(2)
01010101 -> s(3)
11110100 -> s(4)

encoded variable:
10011101 -> e(1) = s(1)
11101001 -> e(2) = s(2) & s(1)
00100001 -> e(3) = s(3) & s(2)
01011110 -> e(4) = s(4) & s(3)
e(n) = s(n) & s(n-1)

decoded variable (same as original string variable)
10011101 -> s(1) = e(1)
10001011 -> s(2) = e(2) & s(1)
01010101 -> s(3) = e(3) & s(2)
11110100 -> s(4) = e(4) & s(3)
s(n) = e(n) & s(n-1)

On the paper it is OK & without any problem, but I can't convert this to c++ source code.
Can you do this?

And... I'm wondering is it possible to do this with OR operator? for my work, this operator is better than AND.

thanks.

[helios]

Uh... That's not a bitwise AND. 10011101 & 10001011 doesn't give 11101001. It gives 10001001.
That looks more like a bitwise XNOR. Furthermore, if that was bitwise AND, the operation couldn't be reversed with that algorithm.

[David P]

Ohh... sorry!!

can you solve my problem by xnor?

thanks.

[helios]

The key to this problem is doing things in the correct order.
original v:
v[0]
v[1]
v[2]
v[3]

v after encoding:
v[0]
v[0]^~v[1]
v[0]^~v[1]^~v[2]
v[0]^~v[1]^~v[2]^~v[3]

Result of applying

for (i=1;i<n;i++){
    v[i]^=~v[i-1];
}

for decoding:
v[0]
v[1]
v[0]^~v[2]
v[1]^~v[3]

I think you should have enough to figure it out.