CompE270_101_Exam1SolutionsAnnotated

CompE270_101_Exam1SolutionsAnnotated - €30 CompE 2'70...

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Unformatted text preview: €30 CompE 2'70 Digital Systems 810 NAME: S0 to ‘ékmg Exam #1 - use additional sheets if needed -- SHOW WORK for partial credit 1) Binary notation has a range of valid values which depends on the number of bits and format. What is the range of valid values (in decimal notation) for: 5 pts. 8 bi ts , unsigned 4 bi ts , 2 ’ s complement 0 (most 23' ,8 from: (base 10) negative) from: 'H ’ (base 10) / ‘5 I -; + to: { (base 10) (to most to: 2"”. 7 (base 10) 25 # II positive) 2) Subtract the 8—bit UNSIGNED values (show results as 8 bits: binary, hex, and decimal notation). Indicate if the result is valid 10 pts FF hex I 1t l \ lll‘ binary = Dec — 10 hex 00010600 binary= Dec show results in I = I: I l O {l 1 1‘ binary = Dec hexadecimal: t F Result valid? 2243 decimal: Borrow Out: ‘0 Overflow: MD 3) Add the 8—bit Mp values (show results as 8 bits: binary, hex, and decimal notation} . Indicate if the result is valid 10 pts 1 t i \ FF hex "" 'l l X \ \\ l \ binary = " ‘ Dec + 10 hex + DOOL 000 0 binary = + I' (0 Dec show results in = 00 O o l \ K \ binary = ‘l’ Dec hexadecimal: (A of: Result valid? 225 decimal: [ i 00‘ 1‘ 010 l '% Carry Out: C = Overflow: x 00 [L 00 t K 4) Multiply 310 times 510 in unsigned binary: W 5 ts \ I, L \ \ P a? 1A 1 1 1 x1, x \ . \ D A _L '______.—--"" fr- Convert: {5 pts ea) —22 2.7, _# S- 5) 4 bit 2's complement 10.51%. to decimal: (a? '6 L we ‘\ _.L 7 o \ “B +l:~“¥x1 dart-“1.75 filly, 6) Decimal —1.25 to 2’s complement binary: ,5 l +1.25»; ownz ~z aw e 43+; I [/4— ZfiCm‘i.’ 10 [DH -: [0.11 7) Unsigned hex 100C to decimal: flog l>c{¢3’+c>+ *2 + D, 4oae+lz 8) Decimal 127 to unsigned hex: 117,323,; In? song! : 7e; Exam1.doc 1 NAME: alugkd YILS CompE 270 Exam 1 9) For the following truth table: 10 pts List the minterms: 21M } + Ed: Dfir } List the maxterms: I'IM( 2);; g}? ) I Hdtofildr ) Include the don’t care terms in the lists above. and then Fill the Label the columns and rows, minterms into the K—map: a 6*- an 4- w- (‘3 F ‘3 Write the equations showing *ALL* terms lb! 5: Minterms(SOP}: y = Q C— 4 Q C. Maxterms(POS}: y = (CHH4Q(Ds+b‘+qlxat\tbl+cxcf+ EH C} Group and circle the ls in the K—map: Write the singlified SOP form of the eqn: y = ! I With the simplified SOP equation, what will the l y output be for the don’t care conditions: 0,4 ? y(O) Draw the logic schematic for the simplified equation: 10) Is this corregtzflfig:£:g;:iij 5 pts //,/ngh the gates a AH Ef:::_ C 0:, M04 jaw 9:60:01 Ago / 6”“0 H f” C Exam1.doc CompE 270 NAME: , £9UJ110MS Exam 1 ll) Fill in the missing term numbers and the row and column values for the 3 and 4 input K—map: 5 pts 12) Write the SOP/PCS equations corresponding to the schematic shown: 10 pts SOP form: I If; I y = q‘b’c +61 bc+qbc +Q6Q 00\ o\\ \06 \0\ List all the minterms: Sm( I_J:3/ 4J 5/ 2 P08 form: y = (Q1—brch-t—6-Fécfli1‘ bI+C3<CLJ+6 fa!) 0000\6 \\O \ \ \ f P’— W I — List all the maxterms and fill in Kemap: y = um Dill: LIT) H Y Min SOP equation form: Gates: f I y=0kC+O~b (L C" ‘12 ‘Oé‘ O\ 1 v Min POS equation form: Gates: I r y=(q+°\(“b) ‘c‘ y a.—‘ \g Exam1.doc b 3 M7 CompE 270 Exam 1 10 pts +0010" 0 0 l l 0 l 0 1 O l l l BCD BCD Resultol‘tD 0016 BCD l4} True/False 2 pts each T/F Equation E x+0=/e’>< _’T: x+x=x r x+xv=,X/\ "1—, X+Y=Y+X E (XYZ)={X’ + Y’ + Z')’ L +LL 11; T/ I11 I I E I I 15) Convert the following binary values to an ASCII character string, ASCII table provided. 10 pts Binary: 10 *ll 11 ll 11 11 11 Cl 0011 111. 0010 0010 0101 0011 0100 000: Hex: 4-3 (of; 31%. 5:53 74- 2_l The symbols are C O Y‘ 'r a C {- Exanfl.doc ( using the hex— NAME: 13) Calculate the following using 4—bit BCD sum, and Show the decimal equivalents: Decimal Decimal Decimal Equation = 0 =x XOX’=}(”/C> Z) Z} 55 5? 53 59 . 5A SB 50 50 '5E 5F 60 '61 62 63 64 65 66 a? 63 59 BA BB 60 an 5E 6F 70 N 72 73 74 75 76 7? 78 79 7A ?B 70 TD 7E 7F X+YZ= (X+Y}{X- (X’Y’Z’J’ = (X + Y — HEX-A8011 mama no NUL 213 + 01 80H 20 ' 02 STX 2D — 03 ETX 2E . 04 EDT 2F 1 05 ENG 30 o 05 ACK 31 1 07 BEL 32 2 ca BS ‘ ‘ 33 3 09 HT 34 4 04 LP 35 5 as VT. 35 5 oc FF 3? 7 00 CF! 38 a GE so 39 9 OF SI 3A : 10 DLE as ; 11 001 (X-ON) 30 < 12 002 (TAPE) 3:: = 13 003 (X—OFF} 3E > 14 004 fine;- 3F ? 15 NAK 40 a 16 SYN 41 A 17 era 42 B 18 CAN 43 c 19 EM 44 D 14 sue 45 E 18 E80 46 F 10 F8 47 G 10 GS 48 H 15 RS 49 | 1F us 414 J 20 SP 48 K 21 1 40 L 22 " 40 M 23 1% 4E N 24 a; 4F 0 25 0/9 50 P 25 a 51 o 2? I 52 R 2a ( 53 S 29 3 54 - T 24 - 55 u -. Ufu—-~Nt<x5<c"mnnuoza—wh'm-‘J‘mfima1oam ,l >L—4/P—1N-<x€< EL CompE 2'70 NAME: ngLUS Exam 1 16) Full adder: (use additional sheets if necassary) 50 Points total, allocated: 5 pts a) Draw the block diagram for a full adder {just inputs and outputs} 5 b} Fill in the truth table showing inputsIr sum and carry outputs 5 c) Draw K—maps for sum and carry out 10 d) Write the minimized SOP equations for the sum and carry outputs 10 e) Draw the schematic from the minimized SOP equation 5 f) Draw the schematic using 2 input XOR gates where appropriate 10 g) Draw a Zebit adder/subtractor made from full adders + gates $3 Cod-r3 L‘s-fiasw SoM‘. a. b 7530 ms Exam1.oc ...
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CompE270_101_Exam1SolutionsAnnotated - €30 CompE 2'70...

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