chap03 - reading it off the truth table. (3.1) ABC + ABC +...

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Last updated: 9/23/2006 ECEn/CS 224 Chapter 3 Homework Solutions 3.1 Draw the truth table for a 3-variable function whose output is TRUE any time an odd number of its nputs is TRUE. A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 3.2 Draw the truth table for a 4-variable function whose output is TRUE any time an even number of its inputs is TRUE. A B C D F 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1
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Last updated: 9/23/2006 3.3 Draw the truth table for a 4-variable function whose output is TRUE any time its inputs, when interpreted as the bits of a 4-bit unsigned binary number, is a multiple of 3 (consider 0 to be a multiple of 3). A B C D F 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 3.4 For each of the problems above, write the boolean equation for the function by
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Unformatted text preview: reading it off the truth table. (3.1) ABC + ABC + ABC + ABC (3.2) ABCD + ABCD + ABCD + ABCD + A BCD + ABCD + ABCD + ABCD (3.2) ABCD + ABCD + ABCD + ABCD + ABCD + ABCD Last updated: 9/23/2006 3.5 Prove that the following identity is TRUE using a truth table: AC + AB + BC = AC + AB. This theorem has a name. What is its name? A B C AC AB BC AC+AB+BC AC+AB 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 Since the last two columns are the same, the two expressions are equivalent. This is called the consensus theorem. 3.6 Prove that the following is TRUE by multiplying it out and then simplifying: ( A + BC )( A + DE ) = AA + ADE + ABC + BCDE = A(1 + DE + BC) + BCDE = A + BCDE 3.7 Write the dual for the equality in the previous problem. A(B+C) + A(D+E) = A(B+C+D+E)...
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chap03 - reading it off the truth table. (3.1) ABC + ABC +...

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