Determine the carry bit of carry-sum generated by unsigned MBE multiplier without final addition

Unpredictable value of carry bit in the summation of carry-sum is an annoying issue preventing carry-sum from being applied to designs with sign extension. In this paper, we propose a methodology to determine the carry bit of the carry-sum form output generated by Booth encoded multiplier without final addition. We discover that this carry bit is a constant "1" in traditional unsigned Modified Booth Encoded (MBE) multiplier, which makes carry-sum form applicable to hierarchy multiplier. Detailed proofs and gate level verification of our discovery is given, and experimental results show more than 20% shorter delay and up to 36% improvement in area-time product compared with non-carry-sum designs.