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Computer Science 150 - Fall 1997 - Fearing - Midterm 1

Computer Science 150 - Fall 1997 - Fearing - Midterm 1 -...

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1 of 5 Problem 1 (25 points) Combinatorial Logic [10 pts.] a) You are given the Boolean function . Complete the truth table for . Hint: Simplify . [8 pts.] b) In this problem you will design a combinational circuit which takes an 8 bit number A[7:0] and cal- culates . For example, if the input , then . The circuit is built from 1 bit modules as shown below. Complete the truth table for the module: [2 pts.] c) Draw a logic diagram for functions and Borrow Out. [5 pts.] d) Show how the 1-bit modules would be interconnected to create an 8-bit subtract 1 circuit. A Borrow In Y Borrow Out 0 0 0 1 1 0 1 1 f A B C , , ( ) ABC BC ( ) A C AB ( ) = f A B C , , ( ) f A B C , , ( ) A B C 0 0 0 0 0 1 0 1 0 0 1 1 f A B C , , ( ) A B C 1 0 0 1 0 1 1 1 0 1 1 1 f A B C , , ( ) Y A 1 = A 00001100 2 = Y 00001011 2 = Y Y n A n BI BO A (1 bit module) Borrow In Borrow Out Y
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2 of 5 Problem 2 (25 points) Timing Complete the time diagram for the figure below, assuming unit delays for all gates and inverters (transport delay only), and no delay in the wires. (The dashed lines in the diagram represent missing sections of the timing dia- gram.) Complete the table below with the voltage levels at the specified location in the timing diagram, i.e.,
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