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# K Simulation for Circuit Analysis

IP.com Disclosure Number: IPCOM000080659D
Original Publication Date: 1974-Jan-01
Included in the Prior Art Database: 2005-Feb-27
Document File: 3 page(s) / 28K

IBM

## Related People

Anstett, RH: AUTHOR [+2]

## Abstract

In digital simulation of logic networks, it is often convenient to know whether application of a given input sequence would produce a given logic state on a particular output, caring neither when nor for how long this state exists. An economical method of performing this calculation called K-simulation is described. K-simulation agrees with results of three-valued simulation which uses the value "X" as the initial state of sequential logic.

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K Simulation for Circuit Analysis

In digital simulation of logic networks, it is often convenient to know whether application of a given input sequence would produce a given logic state on a particular output, caring neither when nor for how long this state exists. An economical method of performing this calculation called K-simulation is described. K-simulation agrees with results of three-valued simulation which uses the value "X" as the initial state of sequential logic.

The relationship between K-simulation and three-valued simulation is further characterized, by the fact that K-simulation is optimistic;, that is, in order to make the three-valued simulation agree exactly, it may be necessary to assume unusual (possibly even varying) circuit and wiring delays. Thus, the K-simulation is useful in that if it indicates that a certain state cannot be reached, this conclusion is correct within the constraint of three-valued simulation.

K-simulation uses a four-valued algebra. The meaning of each value is:
X - Unknown, neither logic 0 nor logic 1 state may be reached. 0 - Logic 0 state may be reached, but not the logic 1 state. 1 - Logic 1 state may be reached, but not the logic 0 state.

K - Both 0 and 1 states may be reached.

A combinatorial three-valued function is extended to four values in the following way:

For a given four-valued input vector with n of its elements equal to K create 2/n/ three-valued vectors by replacing the K's with the 2/n/ combinations of 0's and 1's. Evaluate the given three-valued function for each input vector, and save the results in a 2/n/ position vector R. If some element of R is 0 and some other element is 1, then the four-valued function is K. If 0's exist in R but no 1's, the four-valued function is 0. If 1's exist in R but no 0's, the four-valued function is 1. If all elements of R are X, the four-valued function is X.

Sequential functions can also be extended to four values, by expressing the function...