Sequential
logic based
SOs
\label{sequential-logic-based-sos}
Since combinational logic can not effectively be used to implement the
non–linear functions, such as tanh, absolute and exponentiation, the
authors in [4],
[14],
[17],
[15],
[16] have proposed the
stochastic elements based on sequential logic, or Finite State Machine,
which give a novel approach to perform those functions in SC.
X
………
………
………
Figure 3.3: General diagram of linear state transition
Fig.3.3 illustrates a generic linear
FSM transition diagram. In this configuration, there are N =
2K states, where K is a postitive integer; X,
Y are the input and output of this state machine, respectively.
It is assumed that X is a stochastic sequence which represents
the probability in uniform format PX that each bit being logic 1.
Similarly, PY is the probability of observing logic 1 in uniform
representation of the output stochastic sequence.
As we discussed about combinational logic based stochastic operators in
the sections above, there are many functions which are not represented
using the simple operators (Addition, Multiplication, Subtraction,
etc.). As a result, it can not be realized these fuctions without
difficulty. In this part, we will introduce FSM-SOs that can effectively
overcome this problem.
Stochastic
Tanh
Function
\label{stochastic-tanh-function}
… …
… …
… …
Figure 3.4: State transition diagram of Stochastic Tanh function
Fig. 3.4 shows the diagram of
Stochastic Tanh function [4] in
which the output Y only depends on the current states Si:
Y = . 0, 0 ≤ i ≤ N/2 − 1 , where 0
i N 1. (3.7) 1, N/2 ≤ i ≤ N − 1 ≤ ≤ −
This configuration approximates a Tanh function as follows
N
N
e 2 x − e− 2 x