The embodiments herein describe handling overflow that occurs between different portions of a multi-result vector storing results from performing multiple operations in parallel. Rather than using guard bits to separate the various results in the multi-result vector, the embodiments herein describe using overflow monitors to detect and account for overflow that can occur in a multi-result vector that is passed in a chain of arithmetic units. Side band logic evaluates the LSBs in the operands for the reduced-precision operations to generate an expected value of performing the operation and compares the expected value to an actual value of the corresponding bits in the multi-result vector. If the expected and actual values match, then there was no overflow. However, if the values do not match, the side band logic updates the overflow value so that this overflow can be corrected once the final multi-result vector has been calculated.