exam1_f11_soln - a' + b' + c' ) Problem 3. (a) ( ab'c + (...

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ECE 290 S OLUTIONS TO E XAM #1 September 21, 2011 M. C. Loui Problem 1. (a) Convert to binary first: (10111101.00101110) 2 = (275.134) 8 (b) (i) p 8 = x 3 x 2 x 1 x 0 p 4 = x 6 x 5 x 4 x 0 (ii) With the error in position 3, bit p 1 indicates an error since the bits in positions 1, 3, 5, 7, 9, 11 in the received word have odd parity. Similarly, p 2 indicates an error since bits in positions 2, 3, 6, 7, 10, 11 are also odd parity now. Bits p 4 and p 8 do not indicate an error. So the check bits are c 8 c 4 c 2 c 1 = 0011, which represents 3 in binary. Problem 2. (a) Condition (1): b + c . Condition (2): ( c' + a'b' ). (b) First express in POS: So f ( a , b , c ) = ( b + c ) ( c' + a'b' ) . ( b + c ) ( c' + a' ) ( c + b' ) (c) (i) Σ (m 1 ,m 2 ,m 6 ) (ii) a'b'c + a'bc' + abc' (d) (i) Π (M 0 ,M 3 ,M 4 ,M 5 ,M 7 ) (ii) ( a + b + c ) ( a + b' + c' ) ( a' + b + c ) ( a' + b + c' ) (
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Unformatted text preview: a' + b' + c' ) Problem 3. (a) ( ab'c + ( b'd ) ' ) ( a' + c + c ( d + e' )) ( a + b + d' ) (b) ( a + b' + c )( b' + d ) ' + a'c + abd' Absorption ( a + b' + c ) bd' + a'c + abd' DeMorgan, Involution ( a + c ) bd' + a'c + abd' No-Name abd' + bcd' + a'c + abd' Distributivity abd' + bcd' + a'c Idempotence abd' + a'c C o n s e n s u s ( ab + a'c ) ( d' + a'c ) Distributivity Problem 4. (a) (i) pq' + q'r + p'qs' (ii) ( p' + q' ) ( q' + s' ) ( p + q + r ) (b) p'rs' (c) Yes. Both expressions assign 1 to the dont-care in cell 11 and 0 to cell 15. (d) Complement the POS expression for h to obtain an SOP expression for h' . Problem 5. 5.1 (e) 5.2 (d) 5.3 (b) 5.4 (a) 5.5 (c)...
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