function [regions, num_regions] = zrange_1d(xlow, xhigh)

regions = cell(0, 1);
num_regions = 0;
if length(xlow) ~= length(xhigh)
    disp('Numbers of bits not consistent!');
    return;
end
xl = bin2dec(xlow);
xh = bin2dec(xhigh);
if xl > xh
    return;
end
n = length(xlow);

index = find(xlow == '1', 1, 'last');
if length(index) == 1
    for i = index:n
        if xl + 2^(n - i) - 1 <= xh
            num_regions = num_regions + 1;
            tmp_region = xlow;
            for j = (i + 1):n
                tmp_region(j) = '*';
            end
            regions{num_regions} = tmp_region;
            if xl + 2^(n - i) > xh
                break;
            end
            next_xlow = dec2bin(xl + 2^(n - i), n);
            next_xhigh = xhigh;
            [next_regions, next_num_regions] = zrange_1d(next_xlow, next_xhigh);
            for j = 1:next_num_regions
                num_regions = num_regions + 1;
                regions{num_regions} = next_regions{j};
            end
            break;
        end
    end
else
    for i = 1:n
        if 2^(n + 1 - i) - 1 <= xh
            num_regions = num_regions + 1;
            tmp_region = xlow;
            for j = 1:(n + 1 - i)
                tmp_region(n + 1 - j) = '*';
            end
            regions{num_regions} = tmp_region;
            if xl + 2^(n + 1 - i) > xh
                break;
            end
            next_xlow = dec2bin(xl + 2^(n + 1 - i), n);
            next_xhigh = xhigh;
            [next_regions, next_num_regions] = zrange_1d(next_xlow, next_xhigh);
            for j = 1:next_num_regions
                num_regions = num_regions + 1;
                regions{num_regions} = next_regions{j};
            end
            break;
        end
    end
end