# Summing two binary vectors

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Neeraj Chimwal on 24 Mar 2021
Commented: Adam Danz on 25 Mar 2021
How can I add two binary vector say a= 1 0 1, b= 1 1 0?
Using simply '+' gives decimal output. I want the summation in binary.

Fangjun Jiang on 24 Mar 2021
Edited: Fangjun Jiang on 24 Mar 2021
%%
a = [1 0 1];
b = [1 1 0];
s=dec2bin(bin2dec(num2str(a))+bin2dec(num2str(b)))
out=str2num(s(:))
out =
1
0
1
1
Neeraj Chimwal on 25 Mar 2021
That worked. Thanks

Adam Danz on 24 Mar 2021
Edited: Adam Danz on 24 Mar 2021
y = sumbin(a,b) adds two binary values a and b represented by boolean row vectors (1/0, true/false) and returns the results y as a boolean row vector.
log2dec(v) is a helper function called by sumbin() and converts the boolean vectors to binary strings and then to the decimal representation.
Demo:
a = [1 0 1]; % = 5
b = [1 1 0]; % = 6
log2dec = @(v)bin2dec(num2str(v));
sumbin = @(a,b)dec2bin(sum([log2dec(a), log2dec(b)]))-'0';
sumbin(a,b) % = 11
ans = 1×4
1 0 1 1
If you want to add more than 2 binary numbers in the form of boolean vectors,
y = sumbin(a,b,...,n) receives any number of boolean row vectors (1/0, true/false) and returns the results y as a boolean row vector.
a = [1 0 1]; % = 5
b = [1 1 0]; % = 6
c = ; % = 1
d = [1 1 1]; % = 7
log2dec = @(v)bin2dec(num2str(v));
sumbin = @(varargin)dec2bin(sum(cellfun(log2dec, varargin)))-'0';
sumbin(a,b,c,d) % = 19
ans = 1×5
1 0 0 1 1
##### 2 CommentsShowHide 1 older comment
Adam Danz on 25 Mar 2021
@Neeraj Chimwal just FYI, the first part of my answer and Fangjun Jiang's answer are practically the same, there's very little difference.
The second part of my answer shows how to extend the summation to more than 2 binary vectors.
All vectors are arrays but not all arrays are vectors. A vector is 2D with one dimention equal to 1.
These are vectors
A = [1 0 1];
size(A)
ans = 1×2
1 3
B = [1;0;1];
size(B)
ans = 1×2
3 1
These are arrays that are not vectors
C = rand(2,3);
size(C)
ans = 1×2
2 3
D = rand(2,3,4);
size(D)
ans = 1×3
2 3 4