
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
S.C. Lee, "Vector Boolean Algebra and Calculus," IEEE Transactions on Computers, vol. 25, no. 9, pp. 865874, September, 1976.  
BibTex  x  
@article{ 10.1109/TC.1976.1674711, author = {S.C. Lee}, title = {Vector Boolean Algebra and Calculus}, journal ={IEEE Transactions on Computers}, volume = {25}, number = {9}, issn = {00189340}, year = {1976}, pages = {865874}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1976.1674711}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Vector Boolean Algebra and Calculus IS  9 SN  00189340 SP865 EP874 EPD  865874 A1  S.C. Lee, PY  1976 KW  Canonical form KW  fault detection KW  logic design KW  multibus digital systems KW  multivalued algebra. VL  25 JA  IEEE Transactions on Computers ER   
In this paper, binaryvector Boolean algebra, a generalization of ordinary Boolean algebra [6], is introduced. In this algebra, every element is represented by a binary vector and in addition to ordinary AND, OR, and NOT operations, a new operation called the rotation operation which rotates (rightward or leftward) the components of a binary vector is introduced. Moreover, the NOT or COMPLEMENTATION operation is extended to a more general operation called the generalized complement which includes the total complement (ordinary complement), the null complement (no complement), and newly introduced partial complements. Because of this generalization, all axioms and theorems of ordinary Boolean algebra are generalized. In particular, it is shown that DeMorgan's theorem, Shannon's theorem, and the expansion theorem are generalized into more general forms which include their corresponding ordinary version as a special case. It is also shown that any multivalued logic truth table can be represented by a vector Boolean function. Three compact canonical (sumofproducts and productofsums) forms of this function are presented.
Index Terms:
Canonical form, fault detection, logic design, multibus digital systems, multivalued algebra.
Citation:
S.C. Lee, "Vector Boolean Algebra and Calculus," IEEE Transactions on Computers, vol. 25, no. 9, pp. 865874, Sept. 1976, doi:10.1109/TC.1976.1674711
Usage of this product signifies your acceptance of the Terms of Use.