mid2old

# mid2old - = x y x x y y z in product-of-sums form 5 Boolean...

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CSE20 Midterm 2, February 18, 2010, Name 1. Residual Number System (10 points): Show the operation of 11 × 23 in a residual number system with moduli ( m 1 , m 2 , m 3 ) = (7 , 8 , 9). 2. Residual Number System (15 points): Suppose ( x %5 , x %6 , x %7) = (1 , 3 , 5), where symbol % denotes modulus operation. Find the smallest positive integer x that satis±es this system. 3. Boolean Algebra (15 points): Express Boolean function E ( x, y, z ) = ( x + y + z )( x 0 y 0 + xy 0 z ) 0 in sum-of-products form. 4. Boolean Algebra (20 points): Express Boolean function E ( x, y, z
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Unformatted text preview: ) = x y + x [( x + y )( y + z )] in product-of-sums form. 5. Boolean Algebra (20 points): Prove or disprove that for any elements a , b , and c in set B of Boolean algebra, we have the equality: ( a + c )( a + b )( b + c ) = ( a + c )( a + b ). 6. Boolean Algebra (20 points): Reduce the following to an expression of a minimal number of literals (3): E ( a, b, c ) = abc + ac d + bc d + a b c + ab c d + bc d . 1...
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## This note was uploaded on 12/11/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

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