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September 18th, 2014, 12:53 AM  #1 
Newbie Joined: Sep 2014 From: Sweden Posts: 1 Thanks: 0  Boolean Algebra simplify and basic stuff
Hi! I have a course in Digital Design and honestly, i find it super difficult, so instead of getting nowhere i decided make a thread and ask some questions . Can i simplify this boolean equation any further: f(x,y,z) = z(x'+y) + xy'z = z(x'+y+xy') Thanks in advance 
September 18th, 2014, 03:49 AM  #2 
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 
You can verify that $x'+y+xy'=1$ using a truth table. Symbolically, \begin{align} x'+y+xy'&=x'(y+y')+y+xy'\\ &=x'y+x'y'+y+xy'\\ &=x'y'+y+xy'&&\text{since }x'y+y=(x'+1)y=1y=y\\ &=y'(x+x')+y\\ &=y'+y\\ &=1 \end{align} 
September 18th, 2014, 05:56 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  

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