Discrete Math - Counting Theory

[sjaguar13]

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.

 

[Eman]

Try converting AF to a base 10 number.

How many numbers are between 30 and this number?

 

[sjaguar13]

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.

 

[Eman]

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.)