ps1f02soln - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.111 - Introductory Digital Systems Laboratory Problem Set 1 Solutions Issued: Lecture 4 Day Problem 1: Not Graded.
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abd acd Problem 2: b 1. f = ( a + ( b + c )) ⋅( c + ( a ++ d ) ⋅ ( )) i) truth table ii) Karnaugh map 00001 00011 00100 00111 01001 01011 01100 01110 10001 10011 10101 10111 11001 11011 11101 11110 ab cd f cd ab iii) MPS iv) MSP 1 1 1 0 00 10 11 01 10 11 01 00 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 00 10 11 01 10 11 01 00 cd ab 1 1 1 0 00 10 11 01 10 11 01 00 cd ab 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 c f = c + b d + ad f = ( b d ) ⋅ ( )
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2. + + f = ( c + a b ) ⋅ ( c + ( a + d ) ⋅ ( bd ))⋅( c + ( a + b ) ⋅ ( )) i) truth table 00001 00010 00100 00110 01000 01010 01100 01110 10001 10010 10100 10110 11001 11011 11101 11111 ab cd f iii) MSP 1 0 0 0 00 10 11 01 10 11 01 00 cd ab 1 1 0 0 1 0 0 1 0 0 1 0 ii) Karnaugh map cd ab iv) MPS 1 0 0 0 00 10 11 01 10 11 01 00 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 00 10 11 01 10 11 01 00 cd ab 1 1 0 0 1 0 0 1 0 0 1 0 f = a b + bcd f = ( a + b ) ⋅ ( ) ⋅ ( bc ) ⋅⋅ + +
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3. f = w y + wx ⋅⋅ z y + i) truth table 00000 00010 00101 00111 01001 01010 01101 01111 10000 10010 10101 10111 11000 11010 11100 11110 w xyz f iii) MSP 0 0 1 1 00 10 11 01 10 11 01 00 yz wx 0 0 1 0 0 0 1 0 1 1 0 1
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ps1f02soln - Massachusetts Institute of Technology...

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