
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 26th, 2016, 10:20 AM  #1 
Newbie Joined: Sep 2016 From: Manila Philippines Posts: 2 Thanks: 0  Advanced Boolean Algebraic Equations Basic Equations(1&0) 1+1 = 1 1*1=1 1+0 = 1 1*0=0 0+0 = 0 0*0=0 A+1=1 A*1=A A+0=A A*0=0 A+A=A A*A=A A+A'=1 A*A'=0 Basic Equation(Variables) 1) A+AB = A 2) A+A'B = A+B 3) AB+AB' = A Advance Equation(Multivariable) 1) AB+AB'C = AB+AC 2) A'C+B'C+AB = C+AB 3) A'B+B'C+A'C = A'B+B'C 4) ABC+BC'D+ABD = ABC + BC'D =============================================== Note: by using these equations, you can skip on using long solution process and solve long Boolean problems in less than 10 secs (once you master this). =============================================== Sample easy problem: A'B'C' + ABCD' +ABC + A'C' + AB'C'D' + AB'D +AD' + BC'D' + B'D' + AB' first use Basic Equation(Variables) no.1 you will get: ABC + A'C' +AD' + BC'D' +B'D' + AB' next use Advance Equation no.1 you will get: AC + A'C' + AD' + C'D' + AB' then use Advance Equation no.3 you will get: AC + A'C' + AD' + AB = A'C' + A(B+C+D') Easy right? sample difficult problem: AB'C'D + A'BC +B'C'D + B'D + BC' + AC'D + A'CD' answer: A'C + BC' + B'D Last edited by skipjack; September 26th, 2016 at 10:12 PM. 
September 26th, 2016, 12:41 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,553 Thanks: 1403 
When you get older like me you find that remembering formulas (formulae?) is much more difficult than remembering the concepts they are based on. If you truly grok the concepts you can replicate the formulas on demand. The reverse is not at all true. 
October 11th, 2016, 07:59 PM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  Agree with this one. My peers think that I am a trigonometry master, able to use any trigonometry formula learned in High School. In fact, I only know the most basic formulas and derive the more complicated ones from them.


Tags 
advanced, algebraic, boolean, equations, simplification 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
solving a system of Boolean equations ?  Pent123  Abstract Algebra  1  January 14th, 2016 09:46 AM 
Systems of Boolean Equations  Karlen  Complex Analysis  2  March 3rd, 2015 05:48 AM 
Boolean equations  jojoluvsu2  Applied Math  1  August 7th, 2012 08:43 PM 
Algebraic equations  johnny  Algebra  2  August 21st, 2007 07:02 AM 