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Midterm_sol

Midterm_sol - EE 101 Midterm Fall'09 Redekopp...

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1 EE 101 Midterm Fall ’0 9 ● Redekopp Name: ___ Solutions ____________________ Lecture 9:30 / 12:30 / 2:00 Closed Book Score: ________ No calculators are allowed. Show all your work to get full credit. 1. (18 pts.) Number Systems & Arithmetic (12 pts.) a. (6 pts.) Represent -120 10 in the following systems w/ the given number of bits: System (show work for partial credit) 8-bit Signed Magnitude - 64 + 32 + 16 + 8 = 1111 1000 8-bit 2’s complement = -128 + 8 = 1000 1000 16-bit 2’s complement (don’t work too hard) sign extend => 1111 1111 1000 1000 b. (4 pts.) Represent 185 10 in the following bases: System (show work for partial credit) 8-bit Unsigned Binary 128 + 32 + 16 + 8 + 1 = 1011 1001 (Unsigned) Hexadecimal B9 hex c. (8 pts.) Perform the indicated arithmetic operations given the representation systems below to find the 8-bit (not 9-bit) results. (Do not use the borrow method for subtraction, use the 2’s complement method of subtraction.) Show intermediate steps. Finally, state whether overflow has occurred and briefly justify why it has or has not occurred . a.) 2’s comp. system b.) Unsigned binary 00111011 2 10000000 2 00111011 2 01111111 2 + 1 2 10111011 2 11110011 2 + 00110110 2 00101001 2 Overflow: Y / N Why? P + P = N Overflow: Y / N Why? Final Cout = 1
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2 2. (10 pts.) Short Answer a. How many 1-bit wide, 2-to-1 muxes would be needed to build a 2-bit wide, 6-to-1 mux. 1-bit wide 6-to-1 mux requires 5 2-to-1 muxes. to make it 2-bits wide, replicate. = 5 x 2 = 10 muxes b. A 2-level NOR-AND circuit degenerates to what gate? NOR gate c. True/ False : An arbitrary, (single-bit output) logic function of three variables (e.g. F(x,y,z) can always be implemented with only a 2-to-1 mux and a single inverter). d. A 1-to-31 demux requires a minimum of how many select bits? 5 bits e. In a ripple-carry adder (an adder made from chaining full adders), propagation delay is proportional to the individual full adder propagation delay of? 1. The carry-out bit of the full adders 2. The sum bit of the full adders 3. Neither. Delay in a ripple carry adder is constant no matter how many full adders. 4. Both a and b. f. Given a function of 5 variables A[4:0], write the algebraic form of minterm 25. A4 and A3 and A2’ and A1’ and A0 g. What is the 16’s complement of 5C 16 ? FF 5C = A3 + 1 = A4 h. True / False: Given a function, G, of 4-variables: A,B,C,D that is implemented using a 4-to-1 mux whose 2 select bits are tied to A and B as shown below, input i1 of the mux should be connected to: 1. G(1,0,C,D) 2. G(0,1,C,D) 3. C XOR D 4. G(A,B,0,1) Y A B S 1 S 0 I0 I1 I2 I3 G
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