* Some of you have heard my neighbor’s dog bark in a video or two that I recorded. *While I was busy explaining how to do something awesome in Excel, this dog would decide to bark, adding her own two cents to the lesson. Quite a few of my VBA class students have grown used to it. So much that they complain when a lesson doesn’t have a couple of woofs. But I digress.

So coming back, one of the dogs (probably stray) has decided that she should bring her infant puppies and hide them under our terrace stair case. So, now we have 2 cute little puppies barking day long (and very late in to the night) just outside my office window. We have tried hard to get rid of them, but they somehow sneak back in and start barking or crying. So, I will be busy this weekend trying to move them out.

**But that doesn’t mean, you have to live Excel-less for a few days. So I have a homework.**

## OR XOR AND, Get busy this weekend!

Don’t worry. I am not speaking elvish or something. OR, XOR & AND stand for bit-wise operations.

### Binary?!? What binary?

As the saying goes, *“There are 10 types of people in this world. Those who understand binary and those who don’t.”*

If you understand the quotation, then you probably know what bit-wise operations are. If not, then I guess you were too busy during high-school math lessons.

We are pretty comfortable dealing with regular numbers, those that have base 10.

Binary numbers are in base 2. That means, everything is a zero or one. So 5 becomes 101 (that is `1x2`

)^{2}+0x2^{1}+1x2^{0} = 5

### So what are bit-wise operations?

Just as you have plus, minus, multiplication etc. there are few operations in binary world. See this illustration to understand what some of the basic bit-wise operations mean:

## What is the homework then?

Very simple, assuming 2 cells A1 & A2 have binary numbers in them,

**What formulas you would write to produce the AND, OR & XOR of the numbers?**

**Notes:**

- How would you write formulas if your numbers are less than 512?
- How would you write if the numbers are less than 65536?
- What would you do if the numbers are very very large?

## Go ahead and post your answers

This is no ordinary exercise. But probably it will be easier than getting unwanted puppies out of your house. So go ahead and give this a try. And post your answers using comments. I am waiting.

## Some Tips

- Comment by Cameron & subsequent discussion on how to convert binary numbers to decimal
- Chandoo.org Forum question on ANDing Binary numbers
- 5 AND 3 is 1 by Daniel on Excel Hero
- Testing for Either-Or condition in Excel
- And oh yea, before I forget, never feed an unwanted puppy. If it becomes loyal to you, then are you in for trouble.

That is all. I wish you a pleasant weekend then. Mine is going to be noisy for sure.

## 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