Some New Results on Average Worst Case Carry

The previous bound on average worst case carry in a two's complement adder found by Burks et al. [1] is tightened, a bound is established for one's complement adders, and exact expressions for average worst case carry are derived and "experimentally" tested. It is found that an n-bit ripple-carry two's complement adder with carry-completion detection is potentially as fast, on the average, as the old bound indicated an n/√2-bit adder of the same kind would be.