## Combinations of binary indicator

Solved
Occasional Contributor
Posts: 12

# Combinations of binary indicator

Hi everyone,

I would like to generate all possible combinations of three variables each with values 0 or 1 e.g. following using a data step

000

001

010

100

011

101

110

111

what will be a good way to do it?

Accepted Solutions
Solution
‎04-10-2017 09:37 PM
Super User
Posts: 8,081

## Re: Combinations of binary indicator

[ Edited ]

So maybe something like this.

``````data want;
array p[2] _temporary_ (0 1);
array x[3];
do _n_=0 to dim(p)**dim(x)-1;
do i=1 to dim(x);
x(i)=p(1+mod(int(_n_/(dim(p)**(i-1))),dim(p))) ;
end;
output;
end;
drop i ;
run;``````

All Replies
Community Manager
Posts: 3,424

## Re: Combinations of binary indicator

Check out the ALLCOMB function in SAS.  Designed just for such a thing!

Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

Thanks, it's a nice function. But the problem is I have n=2 (0 or 1) but k=3 which doesn't work for ALLCOMB.

Super User
Posts: 13,517

## Re: Combinations of binary indicator

A not terribly bright solution

```data _null_;
do i='0','1';
do j='0','1';
do k='0','1';
comb=cats(i,j,k);
put comb=;
end;
end;
end;
run;
```
Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

Thanks. The need is to have three distinct columns rather than a single column with all possible combinations.
Super User
Posts: 6,757

## Re: Combinations of binary indicator

These combinations are just a sequence of binary numbers.  You don't need any data to do that:

data want;

do i=0 to 7;

result = put(i, binary3.);

output;

end;

drop i;

run;

Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

Thanks, this is a nice little trick. I will have to have 3 different columns for all combinations of 0 or 1.

Super User
Posts: 8,081

## Re: Combinations of binary indicator

For three it is simple.

``````data want;
do a=0,1; do b=0,1; do c=0,1;
output;
end; end; end;
run;
``````
Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

Great! This has promise. If I have two arrays
P = (0 1) and x = (x1 x2 x3) where each of x takes values 0 or 1, how would you do it?

Super User
Posts: 8,081

## Re: Combinations of binary indicator

Not sure what you are talking about at this point.  If you have four variables named P, X1 , X2, and X3 then you could build all combinations using similar DO loops.  If you have two tables and want to join them to produce all possible combinations then PROC SQL does a good job.

``````proc sql ;
create table want as
select *
from P, X
;
quit;
``````

If you really have two vectors and what to manipulate them then use PROC IML. You can do lots of matrix manipulation using a language designed to work with matrices.

Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

Thanks, I have the following data -
Data a;
Array p[2] (0 1);
Array x[3];
I would like the data step operations to produce 8 rows with the unique combinations.
Solution
‎04-10-2017 09:37 PM
Super User
Posts: 8,081

## Re: Combinations of binary indicator

[ Edited ]

So maybe something like this.

``````data want;
array p[2] _temporary_ (0 1);
array x[3];
do _n_=0 to dim(p)**dim(x)-1;
do i=1 to dim(x);
x(i)=p(1+mod(int(_n_/(dim(p)**(i-1))),dim(p))) ;
end;
output;
end;
drop i ;
run;``````
Occasional Contributor
Posts: 12

## Re: Combinations of binary indicator

This is cool. I have devised a similar solution (but less technical) based on Astounding's proposal.

data a;

array p[2] _temporary_;

array x[3];

do i=1 to dim(p)**dim(x);

result = put(i, binary3.);

do j=1 to 3;

x[j]=substr(result,j,1);

end;

output;

end;

drop i j;

run;

☑ This topic is solved.