test - CSC258 Mid-Term Test 2010 February 26 50 minutes 4...

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CSC258 Mid-Term Test 2010 February 26 50 minutes 4 questions 48 marks The value of each question is shown in square brackets. A blank answer is worth about one-third of the marks; to that, marks will be added for readable, relevant, and correct information, and marks will be subtracted for unreadable, irrelevant, or incorrect information. One aid sheet is allowed. There are laws on the next two pages. 1[6] Is associative? Prove or disprove. 2[15] Simplify the following circuit. x y z 3[15] Using any gates you need, implement the falling-edge-triggered T flip-flop defined as follows. T Q clock T Q Q Q 4[12] Draw a time graph to show the state Q A and Q B of the following circuit for at least 6 clock pulses. Its initial state Q A Q B is 0 0 . Note that the flip-flops are falling-edge- triggered T flip-flops as defined in Question 3. clock T T Q A Q B end of test
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Laws of Binary Algebra Only x x excluded middle –( x x ) noncontradiction ( x y ) = x y material (( x = y )= z ) = ( x =( y = z )) associative (( x y ) z ) = ( x ( y z ))
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