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What is the conversion of (110 1100 1111 110012 from its binary expansion to its octal and hexadecimal expansion? Select one: a. (65376)8, (6CFC)16 b. (66374)8, (6C...

Question

What is the conversion of (110 1100 1111 110012 from its binary expansion to its octal and hexadecimal expansion? Select one: a. (65376)8, (6CFC)16 b. (66374)8, (6CFC)16 C (66374)8, (6DFD)16 d. (65376)8, (6DFD)16

What is the conversion of (110 1100 1111 110012 from its binary expansion to its octal and hexadecimal expansion? Select one: a. (65376)8, (6CFC)16 b. (66374)8, (6CFC)16 C (66374)8, (6DFD)16 d. (65376)8, (6DFD)16



Answers

Convert each of the following binary representations into its equivalent base 10 representation: a. 11.11 b. 100.0101 c. 0.1101 d. 1.0 e. 10.01

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.

That's where to write base A representation of these numbers so were converted in from base to base eight. First step is to write the base representation of this number. So for this number we get and when you love with this, you get to 47. Now we have the base be representation of the number. So in order to get the base even presentation, we're going to apply a modified over where we keep doing the iterations until we get this number or of end to be equal to zero. So this is how that looks like. And in the the answer in base eight off to 47 it's just these remainders here read off some of the bottom of So we get 367 as the representation in base eight. We're gonna apply similar process for parts B, C and D. Part B number is 10101010 10 into and like like before we're gonna find the base to representation of this limiter and I'm gonna skip the work and just tell you that it's 2730 next we just supply equals over and these a reiterations that you get like before just for peace in the version of the bottom up to get our answer of five t 52 have you same thing for parts Seeing the before you see, the number is 111 01111 011 base two on DA representation of this number, we yet 305 e three and we're going to apply Euclid are with them. Find the remainders to get this number in basic. And here it innovations that you get when you put algorithm No, Sorry. And the entry get its 7567 for a number represented in B C? No, For your last part, it's a question. The were given ones there. 1101101101 So the base will be representation of this lumber takes a while to solve, But get to one. Eat 45 No, we apply Eclipse are great them and read off these remainders and bottom up to get her answer 5 to 5 to five in Bay ST That's dancer

Okay, so in this question, we want to convert vintages into their finery. Expansions. So to do this, all we need to do is really just keep dividing my two until we get zero. So for three or a 4321 we get, this is equal to to talk about 1 60 That's one. Then we take the 1 60 over. So 1 60 she won is equal to two times by 80. That's right. Then we take the 80 over. So a lei is equal to treat time like 40 plus There 40 is equal to two times by 20 zur and 20 is equal to two time by 10 10. So Zira, 10 is equal to two ton 50 five is equal to your time. By 2 to 1 two, he's equal to treat time by one plus zero one easy to do time by zero plus one So well, that one. So we stopped. So then this is our finery. Expansion one. So we read it in the opposite direction. So 101000123451234 Why I'm in one. No. 10 to 3. So this is You have to do time by 511 plus one by 11 is equal to to return to 55 plus Spahn 255 is it to two times 127 That's 1127 Easy to to type of 63. That's one 63 Is it to Sonny? But two times by 31 one So you want is equal to two times by 15. This one 15 is you. 22 times seven plus one seven. Easy to top three plus one. Three. Easy to do time about one mile. One easy to treat time there plus one. So we read it backwards. So there's 123456789 10. 12123456789 10. Okay, I lost him. 100 63263 sir. Okay, this is going today. Two times. Why is there are 316 plus one 50316 plus zero. Sorry is equal to two times by two. By 158 plus zero, 25158 He's eating too, to time about 12 Why 79 plus zero 12579 Is equal to cheery time. By six 289 plus one 6 to 89 is equal to two time by 31 or all plus one, 3144 is even too two times that one by 72 One 157 to is equal. Thio two ton by 786 That's right. 786 is equal to two tons. Last 393 zero 393 He's equal to 3.3 two times why 196 plus one 196 is equal to Nice to test went 98. Plus there. Now let's go right here. 98 is equal to 249 plus dessert. What nine is equal to Julia Tuttle. Turn to you or plus one. So 34 Easy to two times by 12. What's there. 12. Easy to Syria. Times 606022 times by three that's Yeah. Three. Easy to two times one plus one. One is a Jew, Times zero plus one. Okay, now we read this way and then we'll read this way. So 110 is our This is a So what was your tzar? 100100 123123 Race too nice.

All right. So for problem with three, you're going to use the rule that is the base. Be representation of a number, and it's going to be equal to do like a knot a one a two lipped a k then end the number is gonna be cool to a K Times base rays of our okay. Plus 80 Caymus. One times based, he came in this one. So on and so forth with anyone times the base plus a knot. Okay, so to use this in ermine expansion. So in that a we are expanding the binary number 111 11 to base 10. So binary means that the base is equal to two. Right? Two bass, two number. Okay, so then this 11111 will then be equal to one times two t four plus one times two cubed plus one times two squared, plus one times two to the power of one plus one times to you the power of zero. So this is 16 plus eight plus four plus two plus one, which is equal to 31. So just part alien four parts to this one. Part B wants us to convert. See? 10 00000001 Again, this is based to Okay, So this number that is very equal to one times Teoh to the ninth pause zero times to eight plus zero times Thio seventh. And we're gonna get plus zero times to the six. Your attempts to four did have to the threes or tested and so on. So forth, little mother I really care about is is the last too. So plus, on times Thio I'm zero. And so it's gonna be equal to 512. All the middle ones right are zero. So those just become equals zero and then plus one. So this is equivalent to 513. So four See, we are converting. 101010101 Okay. And again, this is base too, and said this is gonna be equivalent to one times two to the eighth. And they were gonna get plus zero times to the seventh plus one times +26 plus zero times to fifth and not writing these. Your values will be equal to zero on it. So that one times two to be four plus one times two square and plus one times to have heart zero. And so this is equal to 256 plus 64 plus 16 plus for plus one says his equal to 341. All right. So mortgages you have, the nicer the algebra is. And lastly, we are converting the largest of thes values. 1101001 0001 0000 I guess this is equal to one times two u 2 14 and how you get this first number is sort of count number you have. So this would be to zero two to the 12222 to the three for 567 eat 9 10 11 12 13 and 14 in case we have one times to the 14 plus one times 2 to 13 when you get zero times to the 12 we have one times two to the 11th 0 times to the 10th and zero times two to the ninth. But we have plus one times Thio the power elite and then for two to the power of 56 and seven is all zero as we can move on to one times 2 to 4 and for the remaining ones is also zero. So we can go ahead and kind of ignore the rest of these ones. So when we punish this into the cup kit and get 1 16,384 plus 8192 plus 2000 and 48 plus 256 plus 16 and that is equal to 628,896.


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