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UIL test questions

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which of these is NOT equivalent to 1000102 + 1000002 ?

A) 6610

B)1128

C)4216

D)10000102

E)All are equivalent

 

the answer is B because 1000102 + 1000002 = 3410 + 3210 = 6610 = 1028 = 4216 = 1000102

 

Can anyone help explain how these numbers relate to each other?

 

 

DOC120914-12092014150849.pdf

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Those are different bases. Base-2 is binary, that's what answer D is. Answer A is base-10, that's the number system you're used to (decimal). Base-8 is octal, and base-16 is hexadecimal. You can convert a number in one base into any other base.https://www.google.com/search?client=opera&q=convert+numbers+between+bases&sourceid=opera&ie=UTF-8&oe=UTF-8

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They have to have taught you this in class, it's very important in computer science.

 

It's about different systems for representing numbers. Any number can be represented as a sum of powers: http://en.wikipedia.org/wiki/Positional_notation

 

The base of the power is the base of the numeral system. We use 10 in everyday life, but computers use base 2 (binary).

 

Since binary numbers can get really long engineers use octal (base 8) and hexadecimal (base 16) to represent them. Because 8 and 16 are powers of 2, it's really easy to convert between base 2 and these bases. In octal each digit corresponds to 3 binary digits, in hexadecimal each digit corresponds to four binary digits.

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