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Midterm_sol

Midterm_sol - EE 101 Midterm Fall'07 Redekopp...

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1 EE 101 Midterm Fall ’07 Redekopp Name: __ Solutions ______________________________ Lecture 9:30 / 12:30 / 2:00 Closed Book / 90 minutes Score: ________ No calculators are allowed. Show all your work to get full credit. 1. Number Systems (12 pts.) a. Perform the indicated conversions: (B7) 16 = (?) 8 = (?) 2 = (?) 10 B7 16 = 10110111 2 = 267 8 = 128 + 32 + 16 + 4 + 2 + 1 = 183 10 b. Convert the following bit pattern: 10110111 to the corresponding decimal value for each of the following binary representation systems. System Decimal value (show work for partial credit) 2’s complement = -128 + 32 + 16 + 4 + 2 +1 = -73 dec. Signed Magnitude = - 32 + 16 + 4 + 2 + 1 = -55 dec. Excess-3 Decimal Code = (10’s digit) 1011 – 0011 = 8 = (1’s digit) 0111 – 0011 = 4 =84 dec.
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2 2. Short Answer (10 pts.) a. True /False : A 1-to-8 demultiplexer can be used as a 3-to-8 decoder. b. A 2-level NOR-AND circuit degenerates to what gate? NOR c. True / False : A 4-to-1, 2-bit wide mux can be built using 4 individual 2-to-1 muxes. d. A half-adder can be built with only two gates. What are they? XOR and AND e. The function, G = Σ ABC (0,1,5), is to be implemented with a 3-to-8 decoder with active-low outputs and a single additional gate. To minimize the number of inputs to the gate that will produce G, what gate type should be used? Fewer 1’s in the function, thus use a NAND gate (NAND because active-low) f. A 17-to-1 mux requires how a minimum of how many select bits? 4 select bits can only support 16 inputs, thus we need 5 select bits. (n selects, 2 n data inputs) g. True / False : The 74LS85 comparator studied in class will always output a ‘1’ on the A=B output when the two 4-bit number inputs are equal. h. Subtract the following 2’s complement values and state whether overflow has occurred.. 01101101 - 10000000 01 01101101 A + 01111111 +B’ + 00000001 1 11101101 Overflow has occurred since Cin != Cout and P+P=N.
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3. Design a circuit that takes as input a 3-bit, signed magnitude number A = (A 2 A 1 A 0 ) and produces the equivalent number represented in 2’s complement output, B = (B 2 B 1 B 0 ).
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