Asymptotic Approximations for the Number of Fanout-Free Functions

Bender, Butler
1978 IEEE transactions on computers  
With two cosine terms about a third and with three cosine terms about half as many shifts are needed as for an arbitrary 5. The number of additions varies from about a fifth as many at n = 1 to about a fifteenth or sixteenth as many at n = 5. It should be noted that if the processor used to implement this has 4 or 8 bit shifts, the number of shifts is greatly reduced. Also, it should be stated that this can be implemented in hardware with about 30 MSI TTL packs for the case n = 7, r = 2, a = 1,
more » ... and d= 16. Abstract-Expressions are derived for the approximate number of functions realized by various n-variable fanout-free networks. Six recently studied networks are considered. It is shown that the relative number of functions realized by two networks for smal and large n is quite different in certain cases.
doi:10.1109/tc.1978.1675021 fatcat:mr6khpmojfbvxkag4hgcdlqnuu