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Midterm08_Solns - €13 CPEG 202 MIDTERM(808 NAME $3th CMS...

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Unformatted text preview: €13 CPEG 202 MIDTERM (808) NAME: $3th CMS Question #1 (10 pts) Perform the foliowing arithmetic manipulations. (a) (Show all work). Convert '(94)1ot0 binary, and then convert the binary to hexadecimal. It”! ‘53.. LL 2:. 3;. .1... £11. (- 51w 1‘M 1h? o¢my nu as M: at "‘ j 3 W6 ~31 "-‘0 -- Ir 4.3“ .229— 3&3 (b) (Show all work). Perform binary subtraction for (35)“) - (12)“, using 2’s complement. 31 It. 9' ‘t 1 1 K3§L= {roooxflL on: W“ t 0031. XODOH \QooH \OoQJH - oo\\oo —39 +ificwil = kttotoo M Jr \ ’“1 lot M if” I / M an)?” 01%;. fl :b‘m v” 39.1% fart-HM (1&5) CPEG 202: Introduction to Digital Systems Midterm 2003 1 Question #2 (20 pts) Consider a simple car alarm system involving three sensors. “D” is 0 if all doors are CLOSED and 1 if any door is OPEN. “G" is 0 or 1 if the ignition is OFF or ON, respectively. “L" is O or 1 if the headlights are OFF or ON, respectively. The output ALARM should be 1 (HIGH) in the following cases: 1. The headlights are ON while the ignition is OFF. 2. Any door is OPEN while the ignition is ON. g $3 (a) Build the truth table, construct the K-map, and derive the simplified Boolean expression for ALARM. Keep in mind the implementation requested in part (b). l . f i' A '* t L. J: l) i [ i (4' its) (0 I“ B G Look {VP 1‘; (b) Implement the ALARM function using only NOFl gates. Do not use complemented inputs. OPEG 202: Introduction to Digital Systems Midterm 2008 2 Question #3: (20 pts) Adding with a MUX (a) Build the truth table for a full adder. where the outputs are “S” and "C" and the inputs are “”,x “”,y and‘ "'.2 Build the K- -maps for -S and C. Derive the Boolean expreSSIons for S and C in sum- -of- p—roducls as well as "halt- adder friendly” format. MM...m-..__ Mil 3 07+qu ZW’VUtw «an. W—I W (1&3) = (mom * X01 will: I: ma : x311 11(in +LK’Y klfl’h k KY ' \w ' _ it 6‘) . - X‘1{2%\\ .‘, Q‘QMQA 2% (b) Build a full adder circuit using two MUX 3. Do not use complemented inputs. (1 it“) im CPEG 202: introduction to Digital Systems Midterm 2008 3 Question #4 (20 pts) Conventional implementation Forthe function F=C’(B+D)+(A’+B)D+BC 7- (5% + C(D +A’D + Ebb + 99C (a) Build the K-map and obtain a simplified Boolean expression for F. It is not necessary to derive andior shog the truth table for F. <3, 3&3 (b) (Show all work) Implement the function using only 2—input NAND gates. Do not use complemented inputs. Him: One approach is to re-write the two-level AND-OR implementation in terms of only two-input gates. Then insertipush bubbles. F: (BtQ'QtA’i) = ‘B’rln'ficfib Ur M “—fifi. ‘5 . . F A' -— LI -......... o Gr iii—s) mtwcm .1 is W __ 9’ A‘ r ‘" a A i C... #0 \ C. d“ l D W S) E beams ................ OPEG 202: introduction to Digital Systems Midterm: 2003 4 Question #5 (30 points) BCD adder-subtractor ’1') 1‘ (a) Design a circuit that performs the 9’s complement of a single BOD digit. Recall that 9’s Q complement (for base-10 numbers) is analogous to 1'3 complement {for base-2 numbers). Show the truth table and meaps. Derive simplified expressions, and you are not confined to AND, OR, and NOT operations. Sketch the gate level diagram, and minimize the number of gates in your implementation. Do not assume complemented inputs. Ea] is (b) Construct a BCD adder-subtractor circuit using a BCD adder, the 9's complement circuit Q irom part (a), and one other component. In your sketch, use block diagrams for all three components. CLEARLY LABEL AND SKETCH ALL THE CONNECTIONS In 6 OOFK-EQEW; l 6'00: loco KM“): 06 '6 Clt'tl Q01! Ot LO + °|00 010i Y old; 0100 © 5 oliO QC’IK-i ‘l OI ll UULO Sr ‘000 0001 cl |OCJ| 0000 KKKK CPEG 202: introduction to Digital! Systems Midterm 2008 5 (Extra sheet for work) CPE G 202: Introduction to Digital Systems Mimerm 2098 ...
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