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Question 95 Oa -1 0b. 4 0 -4 0d 55...

Question

Question 95 Oa -1 0b. 4 0 -4 0d 55

Question 9 5 Oa -1 0b. 4 0 -4 0d 55



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What bit patterns are represented by the following hexadecimal notations? a. $8 \mathrm{A} 9$ b. $D C B$ c. EF3 d. A01 e. $\mathrm{C} 99$

Okay, so in this expression, we're going to a place, be with seven. So since seven is most pipe, I be I'm gonna do seven times for the C seven and B is race the second Paris. So this blue seven will be raised to the second power. And then in the order of operations, we're gonna first look at the exponents. So this will be seven times seven to the second. Paris just seven times itself inside the parentheses. This will be inside the blueprint C seven times seven is just 49 then 40 times times Another seven will be 343 which is the same thing at seven to the third power.

Okay, so for prom five or converting Octel expansions to binary and I find that the easiest introduced to convert it back to our base 10 first and then in two binaries. So a is US 572 as an Octel digit. Okay, We're gonna use the rule that the base be representation of any number and right that is given as a nod a one, a two to a k, it's gonna be equal to a k a Times B to the power of K plus a came in this one times B to the K minus one and so on until we get to a one times the base plus a knot. Okay, So if we have the octo expansion is 572. This is gonna be equal to then five times eight to the power of two plus seven times eight to the power of one plus two times eight to the power of zero Kalen. This is going to be equal to 320 plus 56 plus to which is 378 7 base 10. He answers 3 78 But we want based too so in base, too, 378 is equal to two times 189 plus zero, and 1 89 is equal to two times might be four plus one. 94 is equal to two times 47 plus zero. 47 is equal to two times 23 plus one 23 years, equal to two times 11 plus one. 11 is equal to two times five plus one. Five is equal to two times to you, plus one two's equal to two times one plus zero, and one is equal to two times zero plus one. I insulted and take thes remaining values and string together, starting with the most recent sui get that The expansion is 10111 101 zero. That would be four binary or base, too. It's going to the same thing with a few of the numbers. So be gives us 1604 for base eight cancer to expand. This is gonna be equal to one times eight. How are three plus six times eight squared plus zero times eight With one, we'll skip that one. They will get four times eight. How's your ness is equal to 900 s. So when we take the binary expansion 900 we get that mine. Hundreds equal to 450 times two plus zero and 450 is equal to two times 2 25 plus zero. 225 is equal to two times 112 plus one. 1 12 Sequel to two times 56 plus zero. 56 is equal to two times 20 eights plus zero 28 is equal to two times for teen plus zero 14 is equal to two times seven 07 is equal to two times three plus zero three is equal to two times one plus one 1/4 cent last 11 is equal to two times zero plus one. Okay, so we start with the last remainder and string them together. Seconds US. 1100000100 for bass two. Okay, so on to the third part, halfway there. In this instance, we are converting 423 base eight. Okay, so this is gonna be equal to if you can imagine 01 and two have above it will get four times eight square plus two times 8 to 1 plus eight. And what is? It's not for 28. It's 4 23 That will make a difference. Okay, so we have 423 here, which is three times eight tires here, and that is going to be equal to 275 in base 10. But so we want based too. So we take to 75 that is equal to two times. 137 plus one. 1 37 is equal to two times 68 plus one. 68 is equal to two times 34. 34 is equal to two times 17. 17 is equal to two times eight plus one eight is equal to two times four. Okay, four is gonna be equal to two times two. Two is equal to two times one, and one is equal to two times zero plus one So that we take thes remainders starting at the bottom and get 100010011 And that is our base to expansion. Okay, lastly, we are apart. D here which gives us 2417 in these eight. And so it's gonna be equal to two times eight to the power of three plus four times eight to the power of two plus one times eight one plus seven times eight car zero and there is equal to 1295 says based 10. We want bass too, so we'll take 1295 which is equal to two times 647 plus one, 647 is equal to two times 323 plus one, 323 years equal to two times 161 plus one. 161 is equal to two times 80 plus one. 80 is equal to two times for e no remainder. Four years is equal to two times 20 with no remainder 20 years equal to two turns. Turn with no remainder and is equal to two terms. Five again. Remainder there Ah, let me have five is equal to two times two plus one more. Tiu is equal to two turns one plus zero and that one is equal to two times zero plus one. So we start with the last one and we go backwards. So our binary expansion be 101 0000111 one cane, that is base two.

So for this problem, we're going to distribute this three to the top part. So we're gonna get a negative 30. Then we're going to have a positive 15 K and then a 36 k squared. Bring down your zero, and then we're going to go ahead and multiply this and make sure you line it up. It's going to end up being over here at negative I k. Where'd then? We're gonna have a positive 2.5 K to the third power and then a six K to the fourth. So taking there's a zero here as well. So just line everything up and combine any like terms that you have and rewrite. In descending order, we're gonna get six K to a force plus 2.5 K to the third plus 31 K squared plus 15 K minus 30 as our final answer

All right. So here we are, examining compliment notation some more, and so we're gonna start with 11001 And so we take a look initially, the first to do, which is a one. So that means it will be negative. Then we take the remaining for, and since it's negative, we reverse them. All right, so we switch our zeros and ones around and then solve it. So this would be two to the power of two plus two to the power 1 to 6. But it's negative. So our answer will be, for part, a negative six. All rights. We'll take a look, then at part B, which is 01101 So this time we have zero front, which means it is positive, not negative. We'll take the remaining for and solve this. This is too cute. Plus two squared plus two powers zero, which is eight plus four plus one is 13. Okay, part See, we aren't given one 00 01 case of stars with a one which means it's negative was put that in our back pocket. For now, we'll take these four 0001 Since It's negative. We have to swamp all the ones and zeros before we sold it, and then we'll get too cute. Plus two squared plus two is equal to eight plus four plus two, which is equal to 14. But it's negative, so it's gonna be negative. 14 for an answer and lastly, for Part D. If 11111 Well, it starts with a one so we know it's negative. We'll take the remaining for. We want to translate those just equal to zero.


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