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de Lugish  has defined efficient algorithms in radix 2 for certain elementary functions such as Y[X,Y/X1/2, Y + lnX, Y.exp (X), etc. His technique requires a systematic 1-bit left shift of a partially converged result, together with two 4-bit comparisons to select a ternary digit for the next iteration. This selection of digits reduces the average number of full precision additions to about 1/3 of those required in conventional schemes . This paper develops modified algorithms in radix 2 which are more efficient when the time for a full precision addition is comparable to the time for a shift and comparison. The modified procedure is developed for Y/X in detail where more than a 40 percent decrease in execution time is achieved for only a marginal increase in cost.