EE101-U3-BooleanAlgebra-Nazarian-Spring12

L and pl or x 0 0 1 1 y 0 1 0 1 z 0 1 1 1 however we

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Unformatted text preview: see that an AND gate implements the negative logic ‘OR’ function 78 Negative Logic OR and AND A negative logic OR function is equivalent to an AND gate A negative logic AND function is equivalent to an OR gate These are the preferred way of showing the N.L. functions because the inversion bubbles explicitly show where N.L. is being converted to P.L. and the basic gate schematics retain their meaning (when we see an AND gate we know we’re doing some king of AND function with the bubbles indicating N.L.) Shahin Nazarian/EE101/Spring 2012 79 Negative Logic Summary Shahin Nazarian/EE101/Spring 2012 80 Circuit Analysis •  Given a circuit, figure out what it does? •  Usually we have to convert… •  Circuit to Equation •  Equation to T.T. –  But this requires plugging in 2n combinations…BAD!! •  Equation to Canonical Sum or Product –  Slightly easier than T.T. What is this circuit doing? Shahin Nazarian/EE101/Spring 2012 81 Circuit to Equations •  Start from the output and work your way back •  Then convert equation to canonical sum or product F = (X+Y’)•Z + X’•Y•Z’ = XZ + Y’Z + X’YZ’ = XZ(Y+Y’) + Y’Z(X+X’) + X’YZ’ = XYZ + XY’Z + XY’Z + X’Y’Z + X’YZ' X’YZ’ + XY’Z + X’Y’Z + X’YZ’ = XYZ = m7 + m5 + m1 + m2 = ΣXYZ(1,2,5,7) Shahin Nazarian/EE101/Spring 2012 82 Converting to Canonical Sum •  3 Steps: 1.  Use distributive property of T8 to convert to SOP form 2.  Then use T10 or T5 to add in missing variables (AND the term with the desired variable OR’ed with its complement) 3.  Redistribute using T8 w(x+yz) Original Expression wx+wyz T8 wx•1•1 + w•1•yz T10 wx(y+y’)(z+z’)+w(x+x’)yz T10 wxyz +wxyz’ + wxy’z + wxy’z’ + wxyz + wx’yz T8 m15 + m14+ m13 + m12+ m11 Shahin Nazarian/EE101/Spring 2012 Minterms in Canonical Sum 83 Converting to Canonical Product •  3 Steps: 1.  Use distributive property T8’ to convert to POS form 2.  Then use T10 or T5 to add in missing variables (OR the term with desired variable AND’ed with its complement) 3.  Redistribute using T8’ w(x+yz) Original Expression w(x+y)(x+z) T8’ (w+0+0+0)(x+y+0+0)(x+z+0+0) T1 (w+xx’+yy’+zz’)(x+y+ww’+zz’)(x+z+ww’+yy’) T5 (w+x+y+z) (w+x+y+z’) (w+x+y’+z) (w+x+y’+z’) (w+x’+y+z) (w+x’+y T8’ +z’) (w+x’+y’+z) (w+x...
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This note was uploaded on 03/13/2013 for the course EE 101 taught by Professor Redekopp during the Spring '06 term at USC.

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