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I couldn't really understand how SDC conditions are applied to minimize the following Boolean Network from Giovanni De Micheli's slide I am studying.

Given:

$$x=a'+b$$ $$y=abx + a'cx$$

Minimize \$fy\$ to obtain \$gy = ax + a'c\$

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    \$\begingroup\$ Where do you get stuck? What does it look like when you substitute the equation for x into the equation for y? \$\endgroup\$
    – W5VO
    Commented Jun 25, 2014 at 23:49
  • \$\begingroup\$ SDCx = ab'x + a'x' +bx', the book says this is used to simplify fy in to gy, I couldn't see that. and If I substitute the equation for x into y, I will remove x which is still in gy. \$\endgroup\$
    – mill
    Commented Jun 26, 2014 at 7:07

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$$ y=abx+a'cx $$ replacing \$x=a′+b\$ & reducing further: $$ y = ab +a'c + a'cb $$ Using rule: \$A+A'B = A+B\$ $$y= ab +a'c $$ $$y= aa' + ab +a'c $$ $$y= ax +a'c $$

You can get the same with K-map also.

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  • \$\begingroup\$ how about using the condition of SDC? SDCx = x'(a'+b) + x(a'+b)' = ab'x + a'x' + bx'. \$\endgroup\$
    – mill
    Commented Jun 26, 2014 at 13:06

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