Help With XOR

[R.a.B.B.i.T]

Google and MSDN didn't yeild much to me about XOR when used with numerical expressions.  I understand how it works with boolean values (thanks to my electronics course), but I still can't figure out how XOR works.  I tried to replicate how XOR works by using the formula (Y = (!A)B + A(!B)), but that didn't turn out to well.  I used the following code to generate the output below:

Code Select Expand

    Dim i As Integer
    For i = 0 To 100 Step 5
        Debug.Print CStr(i & " XOR 5 = " & ((Not i) * 5) + (i * (Not 5)))
        Debug.Print CStr(i & " Xor 5 = " & (i Xor 5))
        Debug.Print vbNewLine
    Next i

0 XOR 5 = -5
0 Xor 5 = 5

5 XOR 5 = -60
5 Xor 5 = 0

10 XOR 5 = -115
10 Xor 5 = 15

15 XOR 5 = -170
15 Xor 5 = 10

20 XOR 5 = -225
20 Xor 5 = 17

25 XOR 5 = -280
25 Xor 5 = 28

30 XOR 5 = -335
30 Xor 5 = 27

35 XOR 5 = -390
35 Xor 5 = 38

40 XOR 5 = -445
40 Xor 5 = 45

45 XOR 5 = -500
45 Xor 5 = 40

50 XOR 5 = -555
50 Xor 5 = 55

55 XOR 5 = -610
55 Xor 5 = 50

60 XOR 5 = -665
60 Xor 5 = 57

65 XOR 5 = -720
65 Xor 5 = 68

70 XOR 5 = -775
70 Xor 5 = 67

75 XOR 5 = -830
75 Xor 5 = 78

80 XOR 5 = -885
80 Xor 5 = 85

85 XOR 5 = -940
85 Xor 5 = 80

90 XOR 5 = -995
90 Xor 5 = 95

95 XOR 5 = -1050
95 Xor 5 = 90

100 XOR 5 = -1105
100 Xor 5 = 97

Where XOR is my calculation [(Not i) * 5) + (i * (Not 5)] and Xor is Visual BASIC's Xor operator.

When, however, I change my equation to [(Not i) * 5) - (i * (Not 5)], my output is the following:

0 XOR 5 = -5
0 Xor 5 = 5

5 XOR 5 = 0
5 Xor 5 = 0

10 XOR 5 = 5
10 Xor 5 = 15

15 XOR 5 = 10
15 Xor 5 = 10

20 XOR 5 = 15
20 Xor 5 = 17

25 XOR 5 = 20
25 Xor 5 = 28

30 XOR 5 = 25
30 Xor 5 = 27

35 XOR 5 = 30
35 Xor 5 = 38

40 XOR 5 = 35
40 Xor 5 = 45

45 XOR 5 = 40
45 Xor 5 = 40

50 XOR 5 = 45
50 Xor 5 = 55

55 XOR 5 = 50
55 Xor 5 = 50

60 XOR 5 = 55
60 Xor 5 = 57

65 XOR 5 = 60
65 Xor 5 = 68

70 XOR 5 = 65
70 Xor 5 = 67

75 XOR 5 = 70
75 Xor 5 = 78

80 XOR 5 = 75
80 Xor 5 = 85

85 XOR 5 = 80
85 Xor 5 = 80

90 XOR 5 = 85
90 Xor 5 = 95

95 XOR 5 = 90
95 Xor 5 = 90

100 XOR 5 = 95
100 Xor 5 = 97

The second equation is CLOSER but still not exact.  I have no idea how to replicate XOR at this point (with numerical arguments), though my boolean model works just fine (same model as the first, but with boolean values instead of integers).

I am having a *lot* of trouble with this, mainly because it's annoying.  Does anyone know about Xor?

[Newby]

xor looks at the bits of two numbers. If one of them is 1, and the other is 0, the result is 1. If both are 0 or both are 1, the result is 0.

Number 1: 1
Number 2: 0
Result: 1

Number 1: 1
Number 2: 1
Result: 0

Number 1: 0
Number 2: 1
Result: 1

Number 1: 0
Number 2: 0
Result: 0

i.e

01011100
01001010
-----------
00010110

That's just off the top of my head. I could be wrong. Only reason I remember this is because if you xor a number by itself, it returns 0.

EDIT -- I'm not sure if you need help with the xor operator in general, or writing your own xor function.

[MyndFyre]

Newby is indeed correct.  You can't get around looking at the bits of a number when calculating XOR.

[Adron]

Google and MSDN didn't yeild much to me about XOR when used with numerical expressions.  I understand how it works with boolean values (thanks to my electronics course), but I still can't figure out how XOR works.  I tried to replicate how XOR works by using the formula (Y = (!A)B + A(!B)), but that didn't turn out to well. 

Replicating it using (!A)B + A(!B) should work well, if you use the appropriate operators; ! = NOT, * = AND, + = OR (as I'm sure you learned in your electronics course):

A XOR B = ((NOT A) AND B) OR (A AND NOT B)

[Grok]

i.e

01011100
01001010
-----------
11101001

!!!!

[Newby]

i.e

01011100
01001010
-----------
11101001

!!!!

Ooh shit. Caught that, and corrected. Thanks Grok. Wow, that was stupid of me.

Even after giving the right description I still manage to fuck it up ...

[R.a.B.B.i.T]

Google and MSDN didn't yeild much to me about XOR when used with numerical expressions.  I understand how it works with boolean values (thanks to my electronics course), but I still can't figure out how XOR works.  I tried to replicate how XOR works by using the formula (Y = (!A)B + A(!B)), but that didn't turn out to well. 

Replicating it using (!A)B + A(!B) should work well, if you use the appropriate operators; ! = NOT, * = AND, + = OR (as I'm sure you learned in your electronics course):

A XOR B = ((NOT A) AND B) OR (A AND NOT B)

Indeed I did, that's why I was able to replicate the boolean XOR with no problem, but should I convert the number to binary first, do the XOR, then convert it back?

@Newby: a little help with XORing numbers (since I didn't learn anything but XORing bools), but mostly writing my own XOR function that will work with numerical arguments.

@The example:
#01011100
#01001010
-----------
#11101001

$5c
$4a
------
$e9

90
74
-----
213

Correct?

[Newby]

@The example:
#01011100
#01001010
-----------
#11101001

$5c
$4a
------
$e9

90
74
-----
213

Correct?

1. Incorrect You're doing AND on the bits.

2. Wrong. 0x5C ^ 0x4A == 0x16

3. Wrong. 90 ^ 74 == 16

And I'm unsure if this is what you want, as I didn't understand what you meant by "numerical arguments"

[R.a.B.B.i.T]

Numerical vs boolean.  Bools are easy since it's only 1 bit.  The bytes/nibbles/words/whatever are what throw me off.

Also, with the hex and decimal values: I just converted them from the binary, but I obviously failed (which is bad, because I have a test on these conversions tomorrow).

[Adron]

@The example:
#01011100
#01001010
-----------
#11101001

1. Incorrect You're doing AND on the bits.

He's not. He's doing XNOR?

[Dyndrilliac]

Newby was saying whatn he was doing (AND) is wrong. If he were doing XOR, the two zeros would have resulted in a zero instead of a one.


0101101011
0110100101
----------------
0011001110

[Adron]

Newby was saying whatn he was doing (AND) is wrong. If he were doing XOR, the two zeros would have resulted in a zero instead of a one.


0101101011
0110100101
----------------
0011001110

If he were doing AND, the two zeros would have resulted in a zero instead of a one too...

0101101011
0110100101
----------------
0100100001

[Grok]

i.e

01011100
01001010
-----------
11101001

!!!!

I cannot figure what it was.  It starts out like XNOR for 7 bits, then the last bit messes that up.

[Adron]

i.e

01011100
01001010
-----------
11101001

!!!!

I cannot figure what it was.  It starts out like XNOR for 7 bits, then the last bit messes that up.

Last bit? 0 and 0 should be 1 for XNOR, just like the first?

[Grok]

i.e

01011100
01001010
-----------
11101001

!!!!

I cannot figure what it was.  It starts out like XNOR for 7 bits, then the last bit messes that up.

Last bit? 0 and 0 should be 1 for XNOR, just like the first?

Oops, weird.  I looked at that 10 times and saw a 0 and 1 in the last column, every time!  (no pun about 10 times either).