Discrete Math - Counting Theory

In summary, there are 126 hexadecimal numbers between 30 and AF. However, if we include 50 and FF, there are 176 numbers. The example in the book uses 50 and FF, which are 11 numbers apart. Since there are 16 hexadecimal numbers, we can calculate that there are 11 x 16 = 176 numbers between them.
  • #1
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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  • #2
Try converting AF to a base 10 number.

How many numbers are between 30 and this number?
 
  • #3
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.
 
  • #4
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.)
 
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FAQ: Discrete Math - Counting Theory

What is discrete math?

Discrete math is a branch of mathematics that deals with discrete objects and structures, rather than continuous ones. It includes topics such as counting, graph theory, and logic.

What is counting theory?

Counting theory is a subset of discrete math that focuses on counting the number of ways to arrange or choose elements from a set. It involves principles such as permutations, combinations, and the multiplication principle.

How is counting theory used in real-world applications?

Counting theory has many practical applications, such as in computer science, data analysis, and cryptography. It is used to analyze and optimize algorithms, make predictions based on data, and secure communication systems.

What is the difference between permutations and combinations?

Permutations are arrangements of a set of objects in a specific order, while combinations are selections of objects from a set without regard to order. In other words, permutations involve rearranging the elements, while combinations do not.

What is the multiplication principle?

The multiplication principle states that if there are m ways to do one task and n ways to do another task, then there are m x n ways to do both tasks together. This principle is used in counting the number of possible outcomes in a series of events or choices.

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