A Symbolic Analysis of Relay and Switching Circuits

45
oonnect the 2nd level tsck down to the zero level as
shown in Fig. 27.
The zero level then also becomes
the 3rd level and the 6th level.
2,5
1,4
0,3,6
a ....---.j....----.---~I11'----~~------..------....-.-... b
~Nith terminal b connected to this level, we have real1zed
the function with a great saving of elements.
Eliminating unnecessary elements tIlo circuit of Fig. 28
1s obtained.
This deVice 1s e3pecia·lly useful if the
8-numbers form an arit~met1c
can sometimes be applied in other cases.
n
n
progression, although it
The fUnctions
l:2Xk end CC 2 X k
)1 Which were shown to require the most
1 io 1
elements for a ser1es~parallel
realization have very
simple circuits when developed in this mann,er. It
n
/Jan be easily shown that if n is even, then!:2Xk is
1
the symmetric function with all the even numbers
for a-numbers, if n is odd it has all the odd numbers
n
for a-numbers. The function ~Xk) I is, of course,
1
just the opcos1te.
Using the shifting down process