EXCEL XOR multiple bits

Question

Okay I have two cells with a string of bits 0111010 and 0101011. I want to XOR the two together so that the resulting cell would be 0010001.

I know you can use this for boolean values

=OR(AND(A1,NOT(A2)),AND(A2,NOT(A1)))

but it doesn't work for a string of bits.

Answer 1

You need to use VBA to do this. If you open VBA, create a new Module and enter the function

Public Function BITXOR(x As Long, y As Long)
    BITXOR = x Xor y
End Function

You can then use the DEC2BIN and BIN2DEC to convert from binary to decimal to run this function. For example:

Cell A1 = 0111010

Cell A2 = 0101011

=DEC2BIN(BITXOR(BIN2DEC(A1),BIN2DEC(A2)))

Answer 2

You can do this with VBA:

Public Function XOR_binary(b1, b2) As String
    Dim len_b1
    Dim len_b2
    Dim len_diff
    Dim i
    Dim bit1
    Dim bit2

    ' see if the two string are the same length. If not, add 0's to
    ' the beginning of the shorter string

    len_b1 = Len(b1)
    len_b2 = Len(b2)
    len_diff = len_b1 - len_b2

    Select Case len_diff
        Case Is < 0
            ' b2 is longer
            b1 = String(Abs(len_diff), "0") & b1
        Case Is = 0
            ' they're the same length
        Case Is > 0
            ' b1 is longer
            b2 = String(len_diff, "0") & b2
    End Select

    XOR_binary = ""

    For i = Len(b2) To 1 Step -1
        bit1 = CInt(Mid(b1, i, 1))
        bit2 = CInt(Mid(b2, i, 1))

        XOR_binary = CInt(bit1 Xor bit2) & XOR_binary
    Next i

End Function

Probably not the best implementation, but it works.

Using your example, A3 contains:

=XOR_Binary(A1,A2)

The resulting string will have the same number of bits as the longest string you pass in.

Answer 3

Here is a solution without using VBA:
=TEXT(SUMPRODUCT(MOD(INT(MID(A1,{1,2,3,4,5,6,7},1))+INT(MID(A2,{1,2,3,4,5,6,7},1)),2),{1000000,100000,10000,1000,100,10,1}),"0000000")

This calculates the bitwise XOR using SUMPRODUCT and TEXT to turn it into a string of bits.

Note: this formula requires both input values to have length 7 (as per your own example) and the output will also have length 7. To allow for different input lengths, simply implement the necessary truncation and/or padding.

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You can choose to use some shorthand definitions:

• define BitPositions as ={1,2,3,4,5,6,7} (7-bit),
• define BitStrings as ={1000000,100000,10000,1000,100,10,1} (7-bit),
• define BitFormat as ="0000000" (7-bit),

then your formula can be made a bit more legible/shorter/cleaner:
=TEXT(SUMPRODUCT(MOD(INT(MID(A1,BitPositions,1))+INT(MID(A2,BitPositions,1)),2),BitStrings),BitFormat)

This also makes it easier to work with larger strings of bits, e.g.:

• define BitPositions as =ROW(INDIRECT("1:32")) (32-bit),
• define BitStrings as =10^(32-ROW(INDIRECT("1:32"))) (32-bit),
• define BitFormat as =REPT("0",32) (32-bit)

Should you wish to implement NOT/OR/AND/etc. then you can get your inspiration from these formulas for the decimal counterparts; here are some more in-depth explanations for XOR with SUMPRODUCT though it also uses decimal inputs.