This week in Formula Forensics we’ll look at, Zebra Stripes and Checker-board Conditional Formatting.
This idea is inspired by a number of posts over the past few years asking about zebra stripes but specifically BobR who in in June 2011, also asked about Checkerboards in the post: Want to be an excel conditional-formatting Rock Star, Comment No. 154.
I got the conditional format for alternating row and column colors,
Is there a conditional format to make it a checkerboard whereas the cell A2 will remove either the conditional for the row or column and then alternately to A4, B1, B3 etc?
Chandoo responded fairly quickly with this Conditional Formatting formula:
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
Unbeknownst to Chandoo I posted this about a minute later:
=ISODD(ROW()+COLUMN())
Both formula correctly answer BobR’s question.
So today we’re going to pull apart Zebra Stripes and Checker Boards and see what makes them tick.
As always you can follow along in a download file here: Download File.
ZEBRA STRIPES
Zebra Stripes as Conditional Formatting is simply applied using a simple formula within Conditional Formatting.
=MOD(ROW(),2)=0
Conditional Formatting requires a formula that returns a boolean “True” to apply a format or a Boolean “False” to not Apply a format.
So the formula is better read as: If MOD(ROW(),2)=0
And If MOD(ROW(),2)=0, the formula will evaluate as True
This is best evaluated as 3 columns on a worksheet.
In cells
B5:B10 The formula =Row() returns the Row Number
C5:C10 The formula =Mod(Row() ,2) returns the Mod of Row Number, divided by 2
The Mod function returns the remainder of the division of the Row Number divided by 2,
So in Row 5, Mod(Row(),2) = Mod(5, 2) = 5/2 = 2 Remainder 1 = 1
and in Row 6, Mod(Row(),2) = Mod(6, 2) = 6/2 = 3 Remainder 0 = 0
D5:D10 The formula =Mod(Row() ,2)=0 checks the remainder against the value 0
This is what evaluates to either True or False depending on the Row number.
Where the Values are True the Format will be applied (Even Rows)
The Conditional Formatting can be applied to Odd Rows If the Formula is slightly altered
=Mod(Row() ,2)=1
Similarly the formatting can be applied to Columns using
=MOD(COLUMN(),2)=0/1
CHECKER BOARDS
RobR received two responses to his Checker-Board Conditional Formatting request.
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
and
=ISODD(ROW()+COLUMN())
Lest see what’s inside these two formula.
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2) =0, MOD( (ROW() -1)*8+COLUMN(),2)=1)
This is a simple If Formula with 3 components
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
If Condition MOD(ROW(),2)=1
Value if True: MOD((ROW()-1)*8+COLUMN(),2)=0
Value if False: MOD((ROW()-1)*8+COLUMN(),2)=1
The If Condition is already known to us, as it’s the same formula used in the Zebra Stripes above.
It evaluates to True when it is on an Odd Row.
So when it is an Odd numbered Row Excel will look at MOD((ROW()-1)*8+COLUMN(),2)=0
And when it is an Even numbered Row Excel will look at MOD((ROW()-1)*8+COLUMN(),2)=1
We can notice that these are the same formulas which have a different ending of =0 and =1
MOD((ROW()-1)*8+COLUMN(),2)=0
This section Takes each Row subtracts 1 and then multiplies this number by 8. This can be expressed as simply as saying multiply the Row * 8.
This will always return an Even Number and could have been simplified to Row()*2
MOD((ROW()-1)*8+COLUMN(),2)=0
The next bit adds the column number to the previous Even Number.
So now this part will be Odd when the column is Odd and Even when the column is Even.
MOD((ROW()-1)*8+COLUMN(),2)=0
The remainder of the formula is the same as the Zebra Stripes formula.
An Odd Number (Odd Columns) in the section above will return a 1 as the result of =Mod(Odd,2)
An Even Number (Even Columns) in the section above will return a 0 as the result of =Mod(Odd,2)
When evaluated against 0 will return True for Even Columns and False for Odd Columns.
Now the exact same happens in the False section of the If formula except that it is evaluated against 1.
=ISODD(ROW()+COLUMN())
I tackled this problem from a different direction to Chandoo.
Knowing that Even + Even = Even and Even + Odd = Odd and that the row and Column Numbers increase in each direction by 1 each Row/Column, it was simply a matter of adding the Row and Column numbers together and checking if it was Odd or Even
The Excel function IsOdd() and IsEven() both return a Boolean “True” if the contents are Odd or “Even” respectively. This negates an external truth check as described above.
This is easily shown by adding a formula to the Checker area
=Row()+Column()
Excel 2003: The above formula won’t work in Excel 2003.
Try this instead =Mod(Row()+Column(),2)=1
If the alternate shading is required a switch to
=ISEVEN(ROW()+COLUMN())
Does the trick.
Excel 2003: The above formula won’t work in Excel 2003.
Try this instead =Mod(Row()+Column(),2)=0
Learn More About Conditional Formatting Here:
http://chandoo.org/wp/2009/03/13/excel-conditional-formatting-basics/
and
http://chandoo.org/wp/2008/03/13/want-to-be-an-excel-conditional-formatting-rock-star-read-this/
and
http://chandoo.org/wp/2008/10/14/more-than-3-conditional-formats-in-excel/
DOWNLOAD
You can download a copy of the above file and follow along, Download Here.
OTHER POSTS IN THIS SERIES
You can learn more about how to pull Excel Formulas apart in the following posts
Formula Forensics 001 – Tarun’s Problem
Formula Forensics 002 – Joyce’s Question
Formula Forensics 003 – Lukes Reward
Formula Forensics 004 – Freds Problem
We Need Your Help !
If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post as Luke did in Formula Forensics 003. or this post.
If you have a formula that you don’t understand and would like explained but don’t want to write a post also send it in to Chandoo or Hui.
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