I’ve introduced a couple of refinements to my Binary Determination puzzle: firstly roughly equal amounts of ones and zeros (previously there were more ones at a ratio of about 2:1); secondly a more concise way of giving the solution

Place a 0 or 1 in each of the empty cells so that in each row and column a pair of 5-digit binary numbers can be read (therefore with decimal values between 0 and 31), such that the product of the two numbers in a particular row or column is shown at the end of that row or column.

Here is an example (using only 3-digit binary numbers), so for instance in the first column, 010 (2) multiplied by 011 (3) is equal to 6, (as there is a 6 at the foot of the first column) and similarly for all of the other columns and rows. Finally, read off the diagonal of each quarter of the grid and convert back into decimal to give the solution (3,3,2,3):

Here is the puzzle: