A week ago Tarun asked a question on the Chandoo.org Forums.
“I have got multiple names in each row and would like to have what name is repeated maximum number of times and how many times?
Eg. Ram, Amita, Obama, Ram, Willi, Ram, Amita, Chandoo, Ram, Willi
Ans: Ram (4 times)”
(The list and answers are edited)
Chandoo responded with a neat Array Formula:
=INDEX(B2:K2,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0)) &
” (“&MAX(COUNTIF(B2:K2,B2:K2))&” times)”
Lets take a look inside this and see how it works
THE EXAMINATION
The formula has two parts separated by a &
=INDEX(B2:K2,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0))
and
&
and
” (“&MAX(COUNTIF(B2:K2,B2:K2))&” times)”
Each part is separate and can be used independently, the & character simply joins the two parts together to make a single string which answers Tarun’s question, Ram (4 times).
Now, lets look at each part.
You can follow along with this forensic examination by downloading the Sample Data File.
=INDEX(B2:K2,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0))
This is a single Index Function with 2 components, being:
a Range B2:K2 and
a Count MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0)
Typically an Index Function uses 3 components
=Index(Array, Row Number,[Column Number])
In this example the Range is a single Row, B2:K2
And so using the Counter in the Row spot has the effect of counting down the first Column and then continuing at the top of the second Column etc
So the formula used:
=INDEX(B2:K2,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0))
Is equivalent to:
=INDEX(B2:K2,1,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0))
Now lets jump ahead to the COUNTIF(B2:K2,B2:K2) bit
If you copy =COUNTIF(B2:K2,B2:K2) to a cell, Press F2 and then evaluate the Formula using F9
You will see that it returns an array. The array is highlighted by the squiggly brackets { } ‘s
={4,2,1,4,2,4,2,1,4,2}
This is the heart of the solution.
What this is showing us is that for each position in the range B2:K2, the count of how many times that cells value occurs in the range B2:K2
So the formula
=INDEX(B2:K2,MATCH(MAX(COUNTIF(B2:K2,B2:K2)), COUNTIF(B2:K2,B2:K2),0))
Is equivalent to
=INDEX(B2:K2,MATCH(MAX({4,2,1,4,2,4,2,1,4,2}), {4,2,1,4,2,4,2,1,4,2},0))
Looking at the MAX({4,2,1,4,2,4,2,1,4,2}) part, this simplifies to 4, the Maximum value of the array (Remember this line, we’ll come back to it later).
So our simplified formula is now: =INDEX(B2:K2,MATCH(4, {4,2,1,4,2,4,2,1,4,2},0))
Now looking at the MATCH(4, {4,2,1,4,2,4,2,1,4,2},0) part of the equation
You can see that Match is looking for the value 4, in the array {4,2,1,4,2,4,2,1,4,2}, which is the First value , Position 1, the 0 requesting that an exact match is found.
So that MATCH(4, {4,2,1,4,2,4,2,1,4,2},0) is equivalent to 1
So our equation =INDEX(B2:K2,MATCH(4, {4,2,1,4,2,4,2,1,4,2},0))
Is now simplified even more to =INDEX(B2:K2, 1)
Index will then look in B2:K2 and will return the first cell or “Ram” in this example.
& “(” & MAX(COUNTIF(B2:K2,B2:K2)) & ” times)”
The second part of the equation is responsible for counting the number of Times Ram occurs and displaying it with some text.
& “(” & MAX(COUNTIF(B2:K2,B2:K2)) & ” times)”
The parts displayed in Red above add the text ( and times) to the Count
Remember the section MAX(COUNTIF(B2:K2,B2:K2)) which was explained above and evaluates to 4 in this case
So the & “(” & MAX(COUNTIF(B2:K2,B2:K2)) & ” times)”
Part evaluates to: ( 4 times)
With the initial & adding it to the text of the first part Ram for the final result – Ram ( 4 times)
LEARN MORE ABOUT ARRAY FORMULAS
You can learn more about Array Formulas at the following links:
http://www.cpearson.com/excel/ArrayFormulas.aspx
http://www.databison.com/index.php/excel-array-formulas-excel-array-formula-syntax-array-constants/
http://office.microsoft.com/en-us/excel-help/introducing-array-formulas-in-excel-HA001087290.aspx
Chandoo.org has several articles on Array Formulas
http://chandoo.org/wp/tag/array-formulas/
FORENSIC FORMULAS
Would you like to see more “Forensic” examination of complex formulas ?
Let us know in the comments below and it may become a regular section at Chandoo.org.
26 Responses to “Get busy this weekend, with OR XOR AND [Excel Homework]”
first solution for AND
The two numbers are in A1 and B1
= SUBSTITUTE (SUBSTITUTE (A1+B1*9*9, 9, 1), 8, 0)
regards
Stef@n
next solution for OR
=1*SUBSTITUTE (A1+A2;2;1)
regards
Stef@n
last solution for XOR
=1*SUBSTITUTE (A1+A2;2;0)
regards
Stef@n
Or you could make use of the VBA logical operators!
Define the following as custom functions
Public Function BITXOR(x As Long, y As Long)
BITXOR = x Xor y
End Function
Public Function BITAND(x As Long, y As Long)
BITAND = x And y
End Function
Public Function BITOR(x As Long, y As Long)
BITOR = x Or y
End Function
and then use them such:
A B =BITOR(A,B) =BITAND(A,B) =BITXOR(A,B)
0101 0100 0101 0100 0001
an another solution for AND
=1*SUBSTITUTE (SUBSTITUTE (A1+A2;1;0);2;1)
note:
the binary numbers are in A1 and A2 !
regards
Stef@n
I was obviously playing hooky at the beach during the bit-wise math lesson – you lost me at “Understanding bit-wise operations” 🙂
After looking at the above solutions, I find my solution silly, but still:
For the following formulae,
Row 1: headers,
Row 2: OR
Row 3: AND
Row 4: XOR
Column 1: Input 1
Column 2: Input 2
Column 3: Result
OR
{=SUM(IF(MID(A2,ROW(OFFSET($A$1,0,0,LEN(A2),1)),1)+MID(B2,ROW(OFFSET($A$1,0,0,LEN(B2),1)),1)>0,1,0)*10^(LEN(A2)-ROW(OFFSET($A$1,0,0,LEN(B2),1))))}
AND
{=SUM(IF(MID(A3,ROW(OFFSET($A$1,0,0,LEN(A3),1)),1)+MID(B3,ROW(OFFSET($A$1,0,0,LEN(B3),1)),1)=2,1,0)*10^(LEN(A3)-ROW(OFFSET($A$1,0,0,LEN(B3),1))))}
XOR
{=SUM(IF(MID(A4,ROW(OFFSET($A$1,0,0,LEN(A4),1)),1)+MID(B4,ROW(OFFSET($A$1,0,0,LEN(B4),1)),1)=1,1,0)*10^(LEN(A4)-ROW(OFFSET($A$1,0,0,LEN(B4),1))))}
@Anup
Please don't consider your solution silly
Firstly, You are the 3rd person to submit an answer
Secondly, The best formula/function is the one that you know and understand.
I think I have a very tedious solution, which people won't have the patience to do except in small numbers.
I used the same problem setup as "Anup Agarwal"
AND =IF(AND(MID(B2,1,1)="1",MID(C2,1,1)="1"),1,0)&IF(AND(MID(B2,2,1)="1",MID(C2,2,1)="1"),1,0)&IF(AND(MID(B2,3,1)="1",MID(C2,3,1)="1"),1,0)&IF(AND(MID(B2,4,1)="1",MID(C2,4,1)="1"),1,0)
OR =IF(OR(MID(B3,1,1)="1",MID(C3,1,1)="1"),1,0)&IF(OR(MID(B3,2,1)="1",MID(C3,2,1)="1"),1,0)&IF(OR(MID(B3,3,1)="1",MID(C3,3,1)="1"),1,0)&IF(OR(MID(B3,4,1)="1",MID(C3,4,1)="1"),1,0)
=IF(OR(AND(MID(B4,1,1)="1",MID(C4,1,1)="0"),AND(MID(B4,1,1)="0",MID(C4,1,1)="1")),1,0)&IF(OR(AND(MID(B4,2,1)="1",MID(C4,2,1)="0"),AND(MID(B4,2,1)="0",MID(C4,2,1)="1")),1,0)&IF(OR(AND(MID(B4,3,1)="1",MID(C4,3,1)="0"),AND(MID(B4,3,1)="0",MID(C4,3,1)="1")),1,0)&IF(OR(AND(MID(B4,4,1)="1",MID(C4,4,1)="0"),AND(MID(B4,4,1)="0",MID(C4,4,1)="1")),1,0)
Sorry my last post was totally messed up
AND
=IF(AND(MID(B2,1,1)="1",MID(C2,1,1)="1"),1,0)&IF(AND(MID(B2,2,1)="1",MID(C2,2,1)="1"),1,0)&IF(AND(MID(B2,3,1)="1",MID(C2,3,1)="1"),1,0)&IF(AND(MID(B2,4,1)="1",MID(C2,4,1)="1"),1,0)
OR
=IF(OR(MID(B3,1,1)="1",MID(C3,1,1)="1"),1,0)&IF(OR(MID(B3,2,1)="1",MID(C3,2,1)="1"),1,0)&IF(OR(MID(B3,3,1)="1",MID(C3,3,1)="1"),1,0)&IF(OR(MID(B3,4,1)="1",MID(C3,4,1)="1"),1,0)
XOR
=IF(OR(AND(MID(B4,1,1)="1",MID(C4,1,1)="0"),AND(MID(B4,1,1)="0",MID(C4,1,1)="1")),1,0)&IF(OR(AND(MID(B4,2,1)="1",MID(C4,2,1)="0"),AND(MID(B4,2,1)="0",MID(C4,2,1)="1")),1,0)&IF(OR(AND(MID(B4,3,1)="1",MID(C4,3,1)="0"),AND(MID(B4,3,1)="0",MID(C4,3,1)="1")),1,0)&IF(OR(AND(MID(B4,4,1)="1",MID(C4,4,1)="0"),AND(MID(B4,4,1)="0",MID(C4,4,1)="1")),1,0)
@stefan,
I just couldn't get your solutions to work.
01010101010 + 01010101110 = 02020210120
what am i doing wrong?
@anup
...I got yours to work!
@Stephen - I get the same, but Stef@an's second solution for AND does work (at least for the test cases I used)
@ Stephen / Rich
yes , you are right ! - only this works:
OR
=1*SUBSTITUTE (A1+A2;2;1)
XOR
=1*SUBSTITUTE (A1+A2;2;0)
AND
=1*SUBSTITUTE (SUBSTITUTE (A1+A2;1;0);2;1)
@Stef@n - You're answer is really smart, I never knew about the substitute function before. Great Work!
Thx Michael 🙂
yes - it is simply easy 😉
if you add 1 and 1 - excel calculate 2
and then you have to substitute the 2 - new = 0 respectively 1
Here is a good resource for people wanting to learn binary and hexadecimal.
http://justwebware.com/bitwise/bitwise.html
Three that weren't asked for:
NOT
=SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A1+A2,0,3),1,0),3,1)
EQV
=SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A1+A2,0,3),2,3),1,0),3,1)
IMP
=SUBSTITUTE(SUBSTITUTE(A1+SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A2,0,3),1,0),3,1),0,1),2,0)
(was using Daniel Ferry's bitwise file to verify against)
@ Kyle
Not only takes one parameter and inverts 0 -1 and 1-0
Took out the +A2
=SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(A1,0,3),1,0),3,1)
Great solutions!
I'll add two:
NAND =1*SUBSTITUTE (A1+A2,2,0)
NOR=1*SUBSTITUTE(SUBSTITUTE (SUBSTITUTE(A1+A2,0,2),1,0),2,1)
This will work for binary numbers of any size (although the text format mask will have to have as many zeroes as there are digits in the longest addend)
Assume binary #s are in C35 & C36, then add and format as text in C37:
=TEXT(C36+C35,"000000000000")
-sum- = 101112211112
AND - SUBSTITUTE 0s for 1s in -sum-, then sub 1s for 2s
=SUBSTITUTE(SUBSTITUTE(C37,"1","0"),"2","1")
OR - sub 1s for 2s in -sum-
=SUBSTITUTE(C37,"2","1")
XOR - sub 0s for 2s in -sum-
=SUBSTITUTE(C37,"2","0")
Just wandered by:
AND:
=SUBSTITUTE(A1+A2,1,0)/2
Clever, Shane. I like that.
[…] post http://www.excelhero.com/blog/2010/01/5-and-3-is-1.html for examples using Sumproduct, and http://chandoo.org/wp/2011/07/29/bitwise-operations-in-excel/ for examples using Text […]
Hi Chandoo,
I am not (yet) really into bitwise calculation, but I am looking for a way to speed up my vba calculation with very big numbers. Would is ben convenient to use bitwise notation for this?
Best regards,
Ronald (the Netherlands)
p.s. love your country!
@Ronald
I'd suggest asking this in the Chandoo.org Forums
https://chandoo.org/forum/
Attach a sample file with an example of some data and describe what you want to achieve