The boolean algebra has similar properties figure

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ebras Distributivity Complement Idempotency Absorption DeMorgan’s laws ´ · 35 Integer Ring ¢ ¢ ´ ´ · ¢ ´ ·¼ ½ ¼ µ ¼ · ¢¢ µ · µ µ· ¢ ¢¢ ´ µ·´ ·´ · µ ¢ µ µ ¢ ¢ ´ · Boolean Algebra | | & & ´ | µ| |´ | µ ´ & µ& &´ & µ &´ | µ ´ & µ|´ & |¼ &½ &¼ ¼ ˜´˜ µ µ — — — — — — — — — ¼ — |´ & µ ´ | µ &´ | µ |˜ ½ &˜ ¼ & | |´ & µ &´ | µ ˜´ & µ ˜ | ˜ ˜´ | µ ˜ & ˜ Figure 2.7: Comparison of Integer Ring and Boolean Algebra. The two mathematical structures share many properties, but there are key differences, particularly between and ˜. Correspondingly, Ô ˆ Õ equals 1 when either Ô ½ and Õ ¼ , or Ô ¼ and Õ ½ . Claude Shannon, who would later found the field of information theory, first made the connection between Boolean algebra and digital logic. In his 1937 master’s thesis, he showed that Boolean algebra could be applied to the design and analysis of networks of electromechanical relays. Although computer technology has advanced considerably since that time, Boolea...
View Full Document

This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.

Ask a homework question - tutors are online