bitstrings = [0 0 1 1 0 0 0;
0 1 0 1 0 0 1;
1 0 1 1 1 0 0;
0 1 0 1 0 0 0;] %for example
You need to transform your [0 1] in offsets [+1 -1], which is simply achieve by 1-2*bitstrings. cumsum that and you've got your y coordinates. simply plot that matrix and matlab will use 1:... for x exactly as you want. By default plot plots by columns, so transpose the matrix beforehand:
plot(cumsum(1-2*bitstrings'))