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244 Practice Test 1

244 Practice Test 1 - nn n-— 4.1 in nu 1(25 points a(16...

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Unformatted text preview: nn- n..-— 4.1: in nu. - 1. (25 points) a. (16 points) Perform the indicated radix conversion either exactly to the precision specified or until the fraction digits repeat. (Indicate repeating strings of fraction digits with an ogerbar.) i. (3 pts.) 103.710 = mg 5 7—K 33‘ 5 r72. 5 l: f, I .7 r2 “ 7 C36< — re— 8 8 5‘ o 8' @— ‘o’? / 3 '7. s , e ) ANSWER: (“’7- J a “I s r Ii“ ii. (8 pts.) (58.6)“; = (?)g (Hint: Use rational fractions, 8.9., %, if converting to decimal first.) ‘5 5(J1)+gt—6— c0734. 8 a *3 G ” '3,o Vfi‘ we 7 '2 F” I 8 ANSWEsz b. (9 pts.) Memory locations X and Y in a 16-bit 2’s complement machine contain the following bit patterns shown in hexadecimal shorthand: 4‘ (X) = ,SBQC (Y) = ’35D0 n.) A rm M 3‘“ Pat - i B i. (5 pts) Perform the 2’s complement subtraction Z = X — Y on the fixed-point integers, ‘ "‘3, g and express your answer as a 4-digit hexadecimal number. (Hint: use 16‘s complement J I'1’ g arithmetic.) — 'E F F 7: ' S ‘5 3.73 9 C Y”; 1 .1120— + c A 3 o ., C A 2 If 2.. ./3 ICC, _*—'"—"c 430 _ - c /"T_ / ANSWER: a = 34‘ CC ii. (4 pts) What striélg of four c(leciiritil digits is packed into location X in excess—3 (XS-3) code? I I O l l r o o 1 f I a D d/ / Mo: 'UD‘D Orro .fC-W r. " 3 ANSWER:JL___ t A g 5 Ir ”\J id “id U‘J W Name: I (10 points) Memory locations X and Y in a machine with an 18-bit word length that represents signed integers and does arithmetic in 1’s complement contain the following bit patterns (shown in octal shorthand): (X) = ’526177 (Y) = [345623 ml peg .3.” pr: Viewing the contents of X and Y‘as fixed-point integers, perform the following indicated 1’s complement integer fixed-point arithmetic operations, indicating (yes or no) for each whether magnitude overflow (Ovfi?) has occurred. Express your answers as (in-digit octal numbers! (Hint: use 7's complement arithmetic.) x I set?) Mg «3 ?‘+S6'2.3 P” _________—__. 1079021 P“ l_{____.r_1 333‘sd’5 Z=X+Y= 074013/ vali’fl—L/ me x X IZEI'QQ Fe—E ‘FWU ____,_____ I" t.‘ 1150353 955 L—l—xJ dim p03 30! 3. [503:9 / Z:X—Y: (5 points) Draw the logic block diagram of an all NAND gate network that implements the same function h(a,b,c,d,e,f,g) as the network shown. (Hint: Do not attempt to write or simplify an overall expresfion for h; simply use block diagram transformation assuming both complemented and uncomplemented variables for all inputs are available.) 43° O-vfl? gig C/ Narne:______,.—_______— 4. (24 points) Consider the switching function f(a, b, c, d) shown below, where 2,; indicates “don’t cares”: f(a,b, c,d) = 2(0, 1,3,11) + 2415, 7, 8, 10) a. (15 points) Select your answers for this part from the following list of possibilities: i Z A. an essential prime implicant B. a. non-essential prime implicant C. not a prime irnplicant D. not an implicant E. none of the above For each product term listed below circle the letter corresponding to the correct answer (taken from the above list of possible answers) specifying how this product: Efrm relates to the above function. 0.; r r _ r a (4) b'cd We D EX if“; (5; b'd’ A B C @151“ M I(E+c){5+d) (3*: j ( a -e 00 b b. (9 points) For the function f(a,b,c,d) above produce the simplest possible all NOR gate imple« 0‘ mentation (with fewest NOR gates plus fewest inputs to those gates) assuming complemented inputs are available. (33”)(Er of)? '4' _ N ame:— _— 5. (13 points) For the switching function whose truth table is shown to the right: a. (5 points) Write the canonical product of sums expression. a. O 0 0 0 1 1 1 1 Answer: f = b. (8 points) Produce a minimal gate all NAND gate realization for this switching func ion assuming only uncomplemented inputs are available. 42 a 5C” a: It 5% 5‘62} ET ‘1“- E6E+EJ _ ~——=—.—— 4—-—~—— pm b-rafi t: fiC-iLL Name:—/—_______ 6. (15 points) Logic circuit analysis. Work parts a. 8:: b. separately. a. (10 points) Write the simplest sum of products expression for the function f(a,b,c,d) implemented by the gate network shown here: (Ema—17%) We???) a 4L .— " .— — .— ,_ C. (“d—aah)c +_((4:C)C) b a :d‘t'fk—‘nt'! it." C CjD—l /' — a {Zoeaatd‘t (Cc+c) attooo. E HIE! Ea HIII Epic-ralC-rKK-TE)E Ir HEP-1'3- F‘ b. (5 points) Write the simplest sum of products expression for the function g(a.,b,c) implemented by the gate network shown: a’ E C .1 El); ._ c _I_ ha GLC 9 19635: LL+Ltzo+o:o ) «a x®0=xor><|= x h_+:)D“ Xé! : 17%" X 0: Y '6' — Name:_..__— __ _ _. _ (8 points) An ENEE 244 student left the following set of intermediate results in a. pl i the Qume—MeCluskey algorithm. Complete the process and list the resulting set of all pli'inilerifn li- cants (whlch continuation of the process finds) for the function g(a.,b,c d e f) under consideratilin (List them in their binary form using the set of symbols {Fix} in a six 5 mb l representation of each prime implicant.) , l y o I10x001~/ (‘5‘) ”wool C 7 1x0001/ W "Tm—0x1 / 1 ‘i - I O ‘« 101x01!L (3’) H M D < 1x1001 xv ? ”I ”'9 5‘ c 110x01 s ? 11x001‘/ S 1x1011 V 1110::1 \/ ”050‘ {YYOQl/ {w10x-f" ...
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