Discrete Math - Counting Theory

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Homework Help Overview

The discussion revolves around counting the number of hexadecimal numbers between two specific hexadecimal values, 30 and AF. Participants are exploring the conversion of these hexadecimal values to decimal and the implications for counting within that range.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss converting hexadecimal numbers to decimal to facilitate counting. There are questions about the correct interpretation of the range and how to accurately count the numbers between the specified hexadecimal values.

Discussion Status

There is an ongoing exploration of the counting method, with some participants providing conversions and others questioning the logic behind the counting process. Multiple interpretations of the counting range are being considered, and some guidance has been offered regarding the conversion process.

Contextual Notes

Participants note discrepancies between their calculations and examples from a textbook, indicating potential confusion about the counting method and the inclusion or exclusion of boundary values in the count.

sjaguar13
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Hexadecimal numbers are made using the sixteen digits 0 - 9, A-F. how many hexadecimal numbers are there between the hexadecimal numbers 30 and AF?

There are 8 numbers between 3 and A, so I got 3 x 16, but I don't really know.
 
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Try converting AF to a base 10 number.

How many numbers are between 30 and this number?
 
30 = 48
AF = 175

126 numbers between

However, the example in the book is 50 and FF and the solution is, 5 and F is 11 numbers away. There are 16 hexadecimal numbers, so there are 11 x 16 hexadecimal numbers.
50 = 80
FF = 255
That comes out to be 174 numbers. That's not 11 x 16.
 
sjaguar13 said:
30 = 48
AF = 175

126 numbers between

However, the example in the book is 50 and FF and the solution is, 5 and F is 11 numbers away. There are 16 hexadecimal numbers, so there are 11 x 16 hexadecimal numbers.
50 = 80
FF = 255
That comes out to be 174 numbers. That's not 11 x 16.

176 includes 50 and FF. 174 excludes 50 and FF.
128 inculdes 30 and AF. 126 excludes 30 and AF. (In your original post you said 3x16, I think you meant 8x16. Also, thanks for catching my mistake, I forgot that 30 was also a hexidecimal number.)
 
Last edited:

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