course mth 151 I am still unsure how you got some of your answers Could you please explain how my answer came out different when the work matched?Thanks a bunch,
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19:23:27 `q001. There are 5 questions in this set. The preceding calculations have been done in our standard base-10 place value system. We can do similar calculations with bases other than 10. For example, a base-4 calculation might involve the number 3 * 4^2 + 2 * 4^1 + 1 * 4^0. This number will be expressed as 321{base 4}. What would this number be in base 10?
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RESPONSE --> 4^2=16 4^1=4 4^0=1 (3*16) + (2*4) +(1*1)= 48+8+1+=57 10^1*5+10^0*7=57 confidence assessment: 3
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19:23:41 In base 10, 3 * 4^2 + 2 * 4^1 + 1 * 4^0 = 3 * 16 + 2 * 4 + 1 * 1 = 48 + 8 + 1 = 57.
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RESPONSE --> self critique assessment: 3
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19:38:39 `q002. What would the number 213{base 4} be in base 10 notation?
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RESPONSE --> 2*4^2+1*4^1+3*4^0= 2*16+4*1+3*1=32+4+3=39 10^1*3+10^0*9=39 confidence assessment: 3
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19:38:47 213{base 4} means 2 * 4^2 + 1 * 4^1 + 3 * 4^0 = 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39.
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RESPONSE --> self critique assessment: 3
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19:53:05 `q003. Suppose we had a number expressed in the form 6 * 4^2 + 7 * 4^1 + 3 * 4^0. This number isn't quite in the form needs to be if it is to be expressed in base 4. This is because we have the numbers 6 and 5, which exceed 4. How would this number be expressed without using any numbers 4 or greater?
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RESPONSE --> 6*4^2=6*16=96 7*4^1=28 3*4^0=3 96+28+3=127 4/127 4/ 31 r3 4/ 7 r 3 4/3 0 33 base4 4^2+4^2+4^0 2(4^2)+4^0 confidence assessment: 2
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20:01:01 7 = 4 + 3 so 7 * 4^1 can be written as 4 * 4^1 + 3 * 4^1 = 4^2 + 3 * 4^1 Since 6 = 4 + 2, we have 6 * 4^2 = 4 * 4^2 + 2 * 4^2. Since 4 * 4^2 = 4^3, this is 4^3 + 2 * 4^2. Thus 6 * 4^2 + 7 * 4^1 + 3 * 4^1 = (4 * 4^2 + 2 * 4^2) + (4 * 4^1 + 3 * 4^1) + 3 * 4^0 =4^3 + 2 * 4^2 + 4^2 + 3 * 4^1 + 3 * 4^0 = 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 3 * 4^0. This number would then be 1333 {base 4}.
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RESPONSE --> Since we have 127 7 is 4*4^1 2 is 4^1 so we need 4^2+ 4^0 Im lost can you help explain this one please self critique assessment: 0 In a given base you can only use digits which are less than the base. 6 and 7 are both greater than the base 4. The number 6 * 4^2 + 7 * 4^1 + 3 * 4^0 uses digits 6 and 7, which are not used in base 4. 6 = 1 * 4^1 + 2 * 4^0. 7 = 1 * 4^1 + 3 * 4^0. Substituting these expressions for 6 and 7 we obtain 6 * 4^2 + 7 * 4^1 + 3 * 4^0 = (1 * 4^1 + 2 * 4^0) * 4^2 + (1 * 4^1 + 3 * 4^0) * 4^1 + 3 * 4^0. (1 * 4^1 + 2 * 4^0) * 4^2 + (1 * 4^1 + 3 * 4^0) * 4^1 + 3 * 4^0 simplifies to 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 3 * 4^0, as shown in detail in the given solution. Tell me in detail, step by step, what you do and do not understand about this explanation, and about the given solution. &&&&&####################I understand that it needs to be 4 or less. so 6=4+2= 4*4^2+2*4^2=4^3+2*4^2 7=4+3=4*4^1+3*4^1=4^2+3*4^1 (4*4^2+2*4^2)+(4*4^1+3*4^1)+3*4^0 4^3+2*4^2+4^2+3*4^1+3*4^0 4^3+3*4^2+3*4^1+3*4^0 64+48+12+3=127 How did you get 1333?I dont understand the answer&&&&&&&& ##################################
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20:06:29 `q004. What would happen to the number 1333{base 4} if we added 1?
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RESPONSE --> 1334 base4 1*4*3+3*4^2+3*4^1+4*4^0= 64+48+12+4=128 I dont understand what is being asked confidence assessment: 0
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20:07:52 Since 1 = 1 * 4^0, Adding one to 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 3 * 4^0 would give us 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 3 * 4^0 + 1 * 4^0 = 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 4 * 4^0. But 4 * 4^0 = 4^1, so we would have 1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 1 * 4^1 + 0 * 4^0 = 1 * 4^3 + 3 * 4^2 + 4 * 4^1 + 0 * 4^0 . But 4 * 4^1 = 4^2, so we would have 1 * 4^3 + 3 * 4^2 + 1 * 4^2 + 0 * 4^1 + 0 * 4^0 = 1 * 4^3 + 4 * 4^2 + 0 * 4^1 + 0 * 4^0 . But 4 * 4^2 = 4^3, so we would have 1 * 4^3 + 1 * 4^3 + 0 * 4^2 + 0 * 4^1 + 0 * 4^0 = 2 * 4^3 + 0 * 4^2 + 0 * 4^1 + 0 * 4^0. We thus have the number 2000{base 4}. &&&&&######adding 1 would give 1*4^3+3*4^2+3*4^1+3*4^0+1*4^0 1*4^3+3*4^2+3*4^1+4*4^0 1*4^3+3*4^2+4*4^1+0*4^0 1*4^3+3*4^2+1*4^2+0*4^1+0*4^0 1*4^3+4*4^2+0*4^1+0*4^0 1*4^3+1*4^3+0*4^2+0*4^1+0*4^0 2*4^3+0*4^2+0*4^1+0*4^0=4^3*2=128 I dont understand how you got the answer 2000 base4&&&&&&&&&&&&&&&&&&&##########
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RESPONSE --> Im kind of lost could you explain please self critique assessment: 0
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20:17:06 `q005. How would the decimal number 659 be expressed in base 4?
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RESPONSE --> 6 is bigger than 4 so 4+2=6 5= 4+1 4+4+1=9 (4+2)*4^-2+(4+1)*4^-1+(4+4+1)*4^0= I am stuck confidence assessment: 0
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20:32:55 We need to express 659 in terms of multiples powers of 4, with the multiple not exceeding 3. The powers of 4 are 4^0 = 4, 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, 4^5 = 1024. We could continue to higher powers of 4, but since 4^5 = 1024 already exceeds 659 we need not do any further. The highest power of 4 that doesn't exceed 659 is 4^4 = 256. So we will use the highest multiple of 256 that doesn't exceed 659. 2 * 256 = 512, and 3 * 256 exceeds 659, so we will use 2 * 256 = 2 * 4^4. This takes care of 512 of the 659, leaving us 147 to account for using lower powers of 4. We then account for as much of the remaining 147 using the next-lower power 4^3 = 64. Since 2 * 64 = 128 is less than 147 while 3 * 64 is greater than 147, we use 2 * 64 = 2 * 4^3. This accounts for 128 of the remaining 147, which now leaves us 19. The next-lower power of 4 is 4^2 = 16. We can use one 16 but not more, so we use 1 * 16 = 1 * 4^2. This will account for 16 of the remaining 19, leaving us 3. This 3 is accounted for by 3 * 4^0 = 3 * 1. Note that we didn't need 4^1 at all. So we see that 659 = 2 * 4^4 + 2 * 4^3 + 1 * 4^2 + 0 * 4^1 + 3 * 4^0.
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this RESPONSE --> I was confused by the earlier problem where we had to add the 4 and 2 because 6 was bigger and I was thinking about another decimal problem where we used negative exponents to show a decimal. I am just a little unsure of myself. I really could use some help. Im just not sure what I am missing. I guess all of it. self critique assessment: 0 659 is not a base-4 number; in preceding examples you were given base-4 numbers. 659 is a base-10 number, which needs to be expressed in base-4. Can you tell me in detail what you do and do not understand about the given solution?
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Can you tell me in more detail what you do and do not understand about my notes and about the given solutions? With this information I can help you understand those things that are giving you trouble.