Seemingly you have already tried to make a SVG file by tracing the image in Inkscape, but with no success.
A fix: Your 100 x 100 pixels image should be scaled to bigger size to make Inkscape believe the dots are rectangles. Scaling it in Photoshop or GIMP to 1000 x 1000 pixels with the "nearest neighbour" resampling does the job. Rectangles get scaled perfectly with no blur.
The tracing result looks perfect:
After ungrouping the black part should be deleted because it's full of holes. It must be replaced by a solid black background shape. Here the traced black part is moved aside:
Delete it after the new one is drawn and placed. Otherwise you would have no way to place the new one exactly.
But why it should be replaced?
Answer: The edges of the holes fit exactly. SVG:s are often rendered so that edges have 1 px wide transparent zone for anti-aliasing. White could be seen through that gap. A solid background shape stops it.
BTW. There's another answer which essentially suggest you to use the scaled bitmap image as is. Not bad, if there's no other reasons to have a vector than make it look sharp.