On the numbers of variables to represent sparse logic functions

— In an incompletely specified function f, don’t care values can be chosen to minimize the number of variables to represent f. It is shown that, in incompletely specified functions with k 0’s and k 1’s, the probability that f can be represented with only p = 2 log2(k + 1) variables is greater than e−1 = 0.36788. In the case of multiple-output functions, where only the outputs for k input combinations are specified, most functions can be represented with at most p = 2 log2(k+1) −1 variables. Experimental data is shown to support this. Because of this property, an IP address table can be realized with a small amount of memory.

• Type: Conference
• Year: 2008
• Where: ICCAD
• Authors: Tsutomu Sasao
• Keywords: Function F, Hardware, ICCAD 2008, Input Combinations, IP Address Table