[RESOLVED] Understanding XOR

[Liquid Metal]

I am trying to understand how XOR works. Why is this equal to 25?

    MsgBox 77 Xor 84

Just testing this:

Public Sub Main()
    Dim intFix As Integer
    intFix = Fix(256 * Rnd)
    Range("A1").Value = intFix
    
    Dim intAsc As Integer
    intAsc = Asc(Mid$("Test", 1, 1))
    Range("A2").Value = intAsc
    
    Range("A3").Value = intFix Xor intAsc
    
    MsgBox 77 Xor 84
End Sub

[si_the_geek]

XOR does a binary comparison - each bit from the numbers is compared, and if either one but not both is true (ie: the bit in one number doesn't equal the bit in the other), the result is a 1.

In binary (thanks Calculator!), 77 is 1001101, and 84 is 1010100.

1001101 <-77
1010100 <-84
0011001 <-Xor (where the bits differ)

..and when converted back to decimal, that value is 25

You can do similar with Or (if either bit is 1, the output is 1), or And (if both bits are 1, the output is 1).


Based on your recent posts, I presume this is to do with encryption - and the reason that Xor is used is that you can 'undo' the encryption by Xor'ing with the known value.

Assuming 77 was the value you are encrypting, 84 is your 'known value', so Xor'ing the result (25) with it actually gets your original value back - but Xor'ing it with anything else will get the wrong value.

[LaVolpe]

Much better explanation than mine which follows only because I already prepared it.

Bit positions from left to right
1 2 4 8 16 32 64
x   x x       x  = 77
    x    x    x  = 84

Taking 77 and XORing it means to add bits if not there or remove if they are there
so 84 laying over 77 while adding would look like following: o=removed, +=added, x=unchanged
1 2 4 8 16 32 64
x   o x  +     o  = 25
And finally, adding these up, we get 1 Or 8 Or 16 which = 25

ORing adds bits if they were not there already

[Liquid Metal]

Excellent explanation. I been searching the web for a clear explanation like this but did not get any.

You can do similar with Or (if either bit is 1, the output is 1), or And (if both bits are 1, the output is 1).

Always the additional stuff that is good to know.

Based on your recent posts, I presume this is to do with encryption - and the reason that Xor is used is that you can 'undo' the encryption by Xor'ing with the known value.

Yes, I really want to understand that CVMichael Dude's code.

College taught me to convert EBCDIC, Binary and DEC without a calculator. Can you direct me to a tutorial because I asked a similar question last week.

Thank You Si

[Liquid Metal]

Much better explanation than mine which follows only because I already prepared it.

Bit positions from left to right
1 2 4 8 16 32 64
x   x x       x  = 77
    x    x    x  = 84

Taking 77 and XORing it means to add bits if not there or remove if they are there
so 84 laying over 77 while adding would look like following: o=removed, +=added, x=unchanged
1 2 4 8 16 32 64
x   o x  +     o  = 25
And finally, adding these up, we get 1 Or 8 Or 16 which = 25

ORing adds bits if they were not there already

I think this might answer my previous question. Let me take a look at it and get back to you if I have any additional questions. Thank you!

[Liquid Metal]

LaVolpe, that is excellent. With that demo, I can compare AND, OR and so on just like Si_The_Geek mention. Now, I understand how you got to the 25.

But, I am still interest to understand how 25 is converted from binary 0011001 without using a calculator.

[si_the_geek]

The bit on the right (when set to 1) has a decimal value of 1, and each bit to the left of it doubles in value - so you simply add the value of the bits, eg:

0  0  1  1 0 0 1
64 32 16 8 4 2 1

so, 16+8+1 = 25

[Liquid Metal]

cool!

I actually found these two articles:
http://www.wikihow.com/Convert-from-Decimal-to-Binary
http://www.wikihow.com/Convert-from-Binary-to-Decimal

Thanks for getting me going on this Si_The_Geek and LaVolpe!

[Liquid Metal]

One last question, when I convert binary to decimal, do i convert binary to hex or decimal to hex?

[Mark Gambo]

One last question, when I convert binary to decimal, do i convert binary to hex or decimal to hex?

It doesn't matter you can convert from Decimal to Octal to Binary to Hex and back to Octal if you want or any combination in between. You don't need to be in one particular base inorder to convert to another base.

[Merri]

You don't really convert anything. They are the same value represented differently.

Binary = 2 base
Decimal = 10 base
Hex = 16 base

In VB code you can't write bits directly, but decimals and hex are supported. When you write...

lngSomething = 10
lngSomething = &HA

... you do the exact same thing. There is no difference in the final compiled code and there is no executional difference. The value is just represented in different base. If binary representation would be supported, the end result would be the same with it.

Basically one uses hex values in VB code to ease understanding the code... like, when you see F, you know all four bits are being active.

' only highest bit remains active if it is there
bytSomething = bytSomething And &H80

' only high order bits remain active
bytSomething = bytSomething And &HF0

' only low order bits remain active
bytSomething = bytSomething And &H0F

' all except the highest bit remain active
bytSomething = bytSomething And &H7F

[Liquid Metal]

Thanks

I actually found this site and it make so much sense now, especially looking at the last table.

http://www.permadi.com/tutorial/numHexToBin/index.html

Merri, I noticed an "H" in your code. Hex only goes up to "F". Is the "H" a VB representation of Hex format?

[Merri]

&H tells the compiler the following values are hex numbers.

[Liquid Metal]

Thank You