Homework Answers
(a). Note that, 
, and 
. Hence, 53 hours before 5 o'clock, the clock reads 12 o'clock.
(b). As 79x12=948, 
. So, 950 hours after 9 o'clock the clock will read 11 o'clock.
(c). As 58×12=696, 
. Also 
. Hence, 703 hours before 2 o'clock the clock will read 7
o'clock.
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Find the time a clock reads using congruences and mod 12 arithmetic: show work! lal 53...
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Arrange the steps in the correct order to solve the system of congruences x 2 (mod 3), x 1 mod 4). and x3 (mod 5) using the method of back substitution Rank the options below Thus, x= 31.2 - 3/4 + 1)2 - 120+5 We substitute this into the third congruence to obtain 12.5 13 mod 5), which implesu li imod 5) Hence, w5v4 and so x 12.5 - 12/5 + 4) - 5 - 60v. 53, where vis an...
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Problem 2. Find a primitive root for 53. Using this, you can devise a bijection α...
Problem 2. Find a primitive root for 53. Using this, you can
devise a bijection α from the integers modulo 52 to the nonzero
integers modulo 53 with the property that α(a + b) = α(a)· α(b)
modulo 53. Explain. Does the law of exponents get involved at all?
Note: For this to work right, you can think of integers mod 52 as
{0, 1, 2, . . . , 51} or as any complete system of residues modulo
52,...
Phil and Bill also noticed that the reflected clock oc casionally showed a sensible time, but...
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Modify the hours stage of figure 10-18 to keep military time (00-23 hours) SECTION 10-4/DIGITAL CLOCK...
Modify the hours stage of figure 10-18 to keep military
time (00-23 hours)
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#8) please explain and show all work
B: Selecting an adult man who works part time 6) At a small four-year college, all freshmen and sophomores are required to enroll in exactly one of the following math classes: Math I, Math I or Math 200 freshmen and 450 sophomores are enrolled in Math I, 350 freshmen and 400 sophomores are enrolled in Math II, and 250 freshmen and 300 sophomores are enrolled in Math l. a) Find the probability that...
Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E...
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Problem 3: (12 points) Using Multiplexers and additional circuitry as needed, design a four bit arithmetic circuit with two selection variables St and So that generates the following arithmetic operations. Draw the logic diagram for two bits of this device Show all the details of your work. Cin0 Cin-1 F A+1 (increment) F A +B+1 F A+B' +1 (subtract) Si So 0 F AB (add) 1 0 FA+ B' F-A -1 (decrement) F A (transfer)
Problem 3: (12 points) Using...
Arrange the steps in the correct order to solve the system of congruences x 2 (mod 3), x 1 mod 4). and x3 (mod 5) using the method of back substitution Rank the options below Thus, x= 31.2 - 3/4 + 1)2 - 120+5 We substitute this into the third congruence to obtain 12.5 13 mod 5), which implesu li imod 5) Hence, w5v4 and so x 12.5 - 12/5 + 4) - 5 - 60v. 53, where vis an...
3. (16 points) Solve the system of linear congruences using the Chinese Remainder Theorem. 4 (mod 11) a 11 (mod 12) x=0 (mod 13) b. (6 pts) Find the inverses n (mod 11), n21 (mod 12), and nz1 (mod 13). Using these ingredients find the common solution a (mod N) to the system. c. (4 pts) 4. (8 points) What is 1!+ 23+50! congruent to modulo 14?
Problem 2. Find a primitive root for 53. Using this, you can
devise a bijection α from the integers modulo 52 to the nonzero
integers modulo 53 with the property that α(a + b) = α(a)· α(b)
modulo 53. Explain. Does the law of exponents get involved at all?
Note: For this to work right, you can think of integers mod 52 as
{0, 1, 2, . . . , 51} or as any complete system of residues modulo
52,...
Phil and Bill also noticed that the reflected clock oc casionally showed a sensible time, but it didn't match UP2 Clock Reflections the actual time. For example2 Phil and Bill were travelling on a tourist bus. There was a 12-hour digital clock at the front of the bus which displayed times from 1:00 to 12:59. They no- ticed that there was a reflection of the clock in a mirror just above it. Usually the display on the reflected clock was...
Modify the hours stage of figure 10-18 to keep military
time (00-23 hours)
SECTION 10-4/DIGITAL CLOCK PROJECT 763 AMPM tens hrs PM CLRN 74160 units hrs O] QB QC ENT QD ENP RCO units hrs 2] units-hrs[3] CLRN Tens of hours PRN Units of hours CLRN FIGURE 10-18 Detailed circuitry for the HOURS section to count tens of hours. The BCD counter is a 74160, which has two active- HIGH inputs, ENT and ENP, that are ANDed together internally to...
#8) please explain and show all work
B: Selecting an adult man who works part time 6) At a small four-year college, all freshmen and sophomores are required to enroll in exactly one of the following math classes: Math I, Math I or Math 200 freshmen and 450 sophomores are enrolled in Math I, 350 freshmen and 400 sophomores are enrolled in Math II, and 250 freshmen and 300 sophomores are enrolled in Math l. a) Find the probability that...
Modern Algebra, MAT 401 Test 3. Show your work (b) 1. Find a solution x E ZOSXsn for the congruence (a) 8x+3= 5 mod 9 8x=l(mod 21) 2. Find the least positive integer that is congruent to: (a) (14+46+65+92Xmod 11) (b) (717)(32)(62)(mods) (c) 62(mod5) 3. Solve the system (a) x = 2(mod 5) em a lx = 3(mod 8) x 4(mod 7) (3x + 2 = 3(mod 8) 4. Solve the system (a) [4][x] + [2][y] = [1] () {[3][x]...
Problem 3: (12 points) Using Multiplexers and additional circuitry as needed, design a four bit arithmetic circuit with two selection variables St and So that generates the following arithmetic operations. Draw the logic diagram for two bits of this device Show all the details of your work. Cin0 Cin-1 F A+1 (increment) F A +B+1 F A+B' +1 (subtract) Si So 0 F AB (add) 1 0 FA+ B' F-A -1 (decrement) F A (transfer)
Problem 3: (12 points) Using...
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