A numerical simulator is developed to assess various design implications of a digital correlator used by a synthetic aperture interferometric radiometer (SAIR). The simulator permits control of the type of digitization, the digitization thresholds with respect to noise power, and the degree of correlation between the two antenna signals which are being cross correlated. Digitization schemes are considered which use 2, 3, 4, and 8 levels. Estimates are made of the increase in inherent radiometer noise (Delta T) due to the digitization. The increase in Delta T is found to depend strongly on the degree of correlation, with higher correlations suffering less increase. In most cases, 3 level digitization is recommended based on this sensitivity consideration. Two levels perform significantly noisier and four levels only slightly cleaner. Several case studies are also considered regarding the need to control the signal level relative to the digitizer thresholds. Automatic gain control circuitry prior to digitization is found not to be necessary, provided the thresholds are preset within a fairly broad region of minimum sensitivity to variations in signal power, and provided the system noise temperature of the radiometer is monitored with reasonable accuracy. It is also found that, under conditions of very high correlation between the two signals, digital correlators hare better SNR performance than analog. Reasons for this behavior are discussed.