BOOLEAN ALGEBRA AXD CIKCUIT DESIGN 281 



(M'ononiie stn'ings possible. Since each contact miust he connected to the 

 remainder of the contact network, minimizing contacts and conseciuently 

 soldered connections means a sa\in,ii; in wiring time and labor. Further- 

 more, if the designer will manipulate the contacts so that the relays can 

 be chosen from a comparatiA'cIy few standardized codes, which are in 

 large demand, it is possibk^ to a\()i(l the expensive stockpiling of mmier- 

 ous special designs having only a limited demand. In addition, using 

 the least numl)er of contacts minimizes the focal points of most relay cir- 

 cuit failures which are the contacts themselves (i.e., dirty or worn con- 

 tacts). 



It might also be noted at this point that electronic combinational or 

 secjuential circuits usually require electronic gatmg networks to perform 

 functions which are completely analogous to those of relay contact net- 

 works. Hence, the same problem of minimization exists. However, in 

 electronic circuits, gate minimization is even more advantageous since 

 the cost per additional electronic gate is much higher than the cost per 

 additional relay contact. 



It is rather obvious that the multiplicity of paths in most combina- 

 tional and seciuential circuits can cause their design to become an ex- 

 tremely difficult and time consuming problem if the contact paths are 

 developed with the aforementioned considerations in mind. 



The circuit designer's usual approach to the solution of such contact 

 minimization and manipulation problems is that of inspection. The 

 method of inspection presupposes a background of considerable experi- 

 ence in that the designer must recognize certain contact network arrange- 

 ments that may allow further rearrangements and thereby he must 

 mentally develop his ow^i rules. In order to check on any of his manipu- 

 lations he must repeatedly redraw the network during this inspection 

 design process. It is evident that this is often a long and tedious method 

 and, depending on the skill of the designer, may or may not result in an 

 optimum or even adequate solution. 



Suitable contact network arrangements often appear only after con- 

 sideration of several alternative schemes and the rearrangements of the 

 network interconnections of these schemes. Realization of this m kes it 

 ciuite evident that any means of obtaining and comparing these various 

 schemes quickly and with a mathematical accuracy which does not 

 require continuous checking of network paths permits a more rapid and 

 complete exploration of the particular problem. Switching algebra, first 

 codified by C. E. Shannon', is the systematic application of G. Boole's^ 



1 C E. Shannon, A Symbolic Analijsis of Relay and Suntching Circuits, Trans. 

 AIEK, 57, 1938. 



^- G. Boole, The Malhetnalical Analysis of Logic (Cambridge 1847) and An In- 

 vestigation of the Laws of Thought (London 1854). 



