tutLN3soln

tutLN3soln - FIT1001 Solutions to FIT1001 Tutorials for LN3...

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FIT1001 Digital Logic Solutions to FIT1001 Tutorials for LN3 Digital Logic Digital Logic – Introduction (* Important to complete) * Exercise 1 Apply Boolean algebra identities to simplify the following Boolean function: ( AB ) A + A ¯ B SOLUTION: De Morgan ( ¯ A + ¯ B ) A + A ¯ B Commutative A ( ¯ A + ¯ B ) + A ¯ B Distributive A ¯ A + A ¯ B + A ¯ B Inverse 0 + A ¯ B + A ¯ B Identity A ¯ B + A ¯ B Idempotent A ¯ B Exercise 2 Show that xy = ( x + y )( x + ¯ y )(¯ x + y ), using (a) a truth table SOLUTION: x y x + y x + ¯ y ¯ x + y ( x + y )( x + ¯ y )(¯ x + y ) xy 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 (b) Boolean identities SOLUTION: Distributive ( x + y ¯ y )(¯ x + y ) Inverse ( x + 0)(¯ x + y ) Identity x x + y ) Distributive x ¯ x + xy Inverse 0 + xy Identity xy 1
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* Exercise 3 Using the gates AND, OR and NOT, design a circuit that takes three binary digits as input, and outputs 1 if an odd number of these digits is 1, and 0 otherwise. That is, the circuit outputs 1 if there is one 1 and two 0s, or three 1s. Otherwise it outputs 0. SOLUTION: Truth table x y z output 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 Sum of products: ¯ x ¯ yz + ¯ xy ¯ z + x ¯ y ¯ z + xyz * Exercise 4 Using the gates NOT, OR, AND and XOR, construct a digital logic circuit to perform the
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tutLN3soln - FIT1001 Solutions to FIT1001 Tutorials for LN3...

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