approaches a true gaussian distribution conversely the statistics of the sum deviates from a true gaussian distribution as n is made smaller the percent error of the fig1 system 39 s binary approximation to a gaussian curve varies over the curve being smallest near the mean and largest further away from the mean in other words for the more likely sums near the mean value of n 2 the binary and gaussian distributions track closely whereas for the less likely sums toward zero or n the binary distribution deviates to a greater extent from a true gaussian curve fig2 illustrates this phenomenon and shows the curve of a less than 5 approximation error for a binary approximation of a gaussian distribution as a function of the number of binary random variables n the ordinate axis is in terms of the distance from the mean of the distribution n 2 and is measured in terms of the number of standard deviations from the mean thus for example at n 50 random variables the binary distribution approximates a true gaussian distribution with less than 5 error out to about three standard deviations on each side of the mean whereas at n 200 random variables a less than 5 error can be expected out to about four and a half standard deviations on each side of the mean one can also plot for a particular number of random variables the percentage error of the binary approximation of a gaussian distribution as a function of the number of standard deviations from the mean for example in fig3 the graphs are for n 28 random variables and the solid curve 15 represents the percentage error plotted as a function of number of standard deviations from the mean for a prior art configuration of the.