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PeterBartholomew1

Silver Contributor

Feb 02, 2024

Working with Binary numbers BASE(..., 2, 7) and bit operations BITXOR, BITAND

I recently came across an Excel challenge from Chinmay Amte on LinkedIn and I plan to post my solution here because it contains some 'off the beaten track' techniques that might be of some interest. ...

Possible Coalitions.xlsx23 KB

excel

Formulas and Functions

office 365

SergeiBaklan

MVP

Feb 03, 2024

PeterBartholomew1

Combinations is too complex for me, make the bookmark to play one day.

As for the binary logic long ago I used it to check if the character is in English alphabet or in digits

ABC = LAMBDA(chr,
    IFERROR(
        BITOR(chr, 48),
        IFERROR(CHAR(BITXOR(CODE(chr), 32)) = chr, 0)
    )
)

and only to play with it, sure could be done other way. No more practical cases in my practice.

PeterBartholomew1
Silver Contributor
Feb 03, 2024
SergeiBaklan
Even that is more than I had expected! I had definitely regarded BITXOR as lying within an exotic but very obscure corner of Excel. Perhaps not as bad as a Bessel function of the second kind, but close. Mind you, the finance formulas have their oddities; DOLLARFR means very little to me!

Presumably the trick in your formula is to move from lower case characters to upper case and the converse.

Resources

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I recently came across an Excel challenge from Chinmay Amte on LinkedIn and I plan to post my solution here because it contains some 'off the beaten track' techniques that might be of some interest.

Post | Feed | LinkedIn
\"Yesterday, Indian state of Bihar was in news due to change in structure of coalition government.
Assume you are an Analyst at Governor's office. He has asked you to evaluate ALL possible combinations of coalition between the political parties to form a government.\"

Please note, minimum vote of 122 is required to form government.
The correct answer for the number of possible combinations is 61 (done manually)!

There are 127 combinations so I started with a decimal index but, within the Lambda functions SeatCountλ and ListNamesλ, this is first turned into a binary number (with 1 indicating that the corresponding party is part of the coalition.

= LET(\n n, COUNTA(party),\n combinations, SEQUENCE(2^n - 1),\n totalSeats, MAP(combinations, SeatCountλ(seats)),\n possible, FILTER(combinations, totalSeats>121),\n coalition, MAP(possible, ListNamesλ(party)),\n seats, MAP(possible, SeatCountλ(seats)),\n HSTACK(coalition, seats)\n )

MID is then used to split the binary number (a string) into separate cells to that matrix multiplication can be used to evaluate the total seats for each coalition.

\"SeatCountλ\"\n= LAMBDA(combination,\n LET(\n n, COUNTA(seats),\n bin, BASE(combination, 2, n),\n k, SEQUENCE(1, n),\n p, SIGN(MID(bin, k, 1)),\n MMULT(p, seats)\n )\n )

I observed that the coalitions identified include cases that have more parties involved than are strictly necessary to form a government. Therefore I set out to discount any coalition that included a viable governing coalition as a subset. That is where the bit operations came into the equation.

Subsetλ\n\"Determines whether the first parameter is a subset of the second \nwhere set membership is determined by digits of a binary number\"\n= LAMBDA(set₁, \n LET(\n diff, BITXOR(set₁, set₂), \n IF(set₁ <> set₂, BITAND(set₁, diff) = 0)\n )\n )

Despite the fact that the concept involves binary numbers, the arguments to BITXOR and BITAND are actually their decimal equivalents. Exclusive BITXOR returns 0 where the corresponding bits match and 1 for mismatches. The bitwise BITAND examines one of the sets to see whether there is any non-zeros where the sets differ. That is does that coalition include any parties that are not in the second, in which case both combinations must be retained.

It is not often I get to use BITXOR etc. Do others have examples of their use?

Just as a final point which may cause reaction from Excel users that hate 'black boxes', my final worksheet formula was no more than

= PotentialCoalitionsλ(party,seats,122)

which gave rise to

I am happy to accept any feedback. It is, after all, well away from looking like a traditional spreadsheet.

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I recently came across an Excel challenge from Chinmay Amte on LinkedIn and I plan to post my solution here because it contains some 'off the beaten track' techniques that might be of some interest.

Please note, minimum vote of 122 is required to form government.
The correct answer for the number of possible combinations is 61 (done manually)!

= LET(\n    n,            COUNTA(party),\n    combinations, SEQUENCE(2^n - 1),\n    totalSeats,   MAP(combinations, SeatCountλ(seats)),\n    possible,     FILTER(combinations, totalSeats>121),\n    coalition,    MAP(possible, ListNamesλ(party)),\n    seats,        MAP(possible, SeatCountλ(seats)),\n    HSTACK(coalition, seats)\n  )

MID is then used to split the binary number (a string) into separate cells to that matrix multiplication can be used to evaluate the total seats for each coalition.

\"SeatCountλ\"\n= LAMBDA(combination,\n    LET(\n        n,   COUNTA(seats),\n        bin, BASE(combination, 2, n),\n        k,   SEQUENCE(1, n),\n        p,   SIGN(MID(bin, k, 1)),\n        MMULT(p, seats)\n    )\n  )

Subsetλ\n\"Determines whether the first parameter is a subset of the second \nwhere set membership is determined by digits of a binary number\"\n= LAMBDA(set₁, \n    LET(\n      diff, BITXOR(set₁, set₂), \n      IF(set₁ <> set₂, BITAND(set₁, diff) = 0)\n    )\n  )

It is not often I get to use BITXOR etc. Do others have examples of their use?

Just as a final point which may cause reaction from Excel users that hate 'black boxes', my final worksheet formula was no more than

= PotentialCoalitionsλ(party,seats,122)

which gave rise to

I am happy to accept any feedback. It is, after all, well away from looking like a traditional spreadsheet.

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PeterBartholomew1

Combinations is too complex for me, make the bookmark to play one day.

As for the binary logic long ago I used it to check if the character is in English alphabet or in digits

ABC = LAMBDA(chr,\n    IFERROR(\n        BITOR(chr, 48),\n        IFERROR(CHAR(BITXOR(CODE(chr), 32)) = chr, 0)\n    )\n)

and only to play with it, sure could be done other way. No more practical cases in my practice.

","body@stringLength":"709","rawBody":"

Combinations is too complex for me, make the bookmark to play one day.

As for the binary logic long ago I used it to check if the character is in English alphabet or in digits

\nABC = LAMBDA(chr,\n IFERROR(\n BITOR(chr, 48),\n IFERROR(CHAR(BITXOR(CODE(chr), 32)) = chr, 0)\n )\n)\n

and only to play with it, sure could be done other way. No more practical cases in my practice.

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SergeiBaklan

Even that is more than I had expected! I had definitely regarded BITXOR as lying within an exotic but very obscure corner of Excel. Perhaps not as bad as a Bessel function of the second kind, but close. Mind you, the finance formulas have their oddities; DOLLARFR means very little to me!

Presumably the trick in your formula is to move from lower case characters to upper case and the converse.

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