# Best way to generate an array of all possible integer numbers for a given base and number of digits

2 views (last 30 days)
Bill Tubbs on 8 Jun 2021
Answered: Walter Roberson on 9 Jun 2021
I want to prepare an array that contains all combinations in rows of possible sequences represented by an d-digit number of base b.
E.g. With n = 3 and b = 2 I came up with the following two ways to do it
d = 3; b = 2; n = b^n-1;
S = dec2base(0:n-1,b) == '1'
S =
7×3 logical array
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
This method works for d <=3 but not higher:
[B1,B2,B3] = meshgrid(0:b-1,0:b-1,0:b-1);
S = [B1(:) B2(:) B3(:)]
S =
0 0 0
0 1 0
1 0 0
1 1 0
0 0 1
0 1 1
1 0 1
1 1 1
The order of the sequences doesn't matter.
I'm sure there must be a simpler way!

Walter Roberson on 9 Jun 2021
d = 4; b = 3;
B = cell(1,d);
[B{:}] = ndgrid(0:b-1);
B = cellfun(@(M) M(:), B, 'uniform', 0);
S = [B{end:-1:1}];
S
S = 81×4
0 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0 0 0 1 1 0 0 1 2 0 0 2 0 0 0 2 1 0 0 2 2 0 1 0 0

R2019b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!