Address range to Mb

Question

Could you explain me the following convertion:

The address range is 0x00100000 to 0x1fffffff

How to convert it to bytes or Mb?

Answer 1

Remember that the following number 0x123 is essentially (Starting from the last digit)

$$3*16^0 + 2*16^1 + 1*16^2 = 3 + 2*16 + 1*256 =291 $$

it is essentially the same what you are doing if you had 123 in the decimal system (just the base changes):

$$3*10^0 + 2*10^1 + 1*10^2 = 3 + 2*10 + 1*100 =123 $$

So in your case, the first number is

• 0x00100000 = 1*16^5 = 1048756

regarding the second number I'd cheat a little bit, so 0x1fffffff = 0x20000000 -1. So with that:

• 0x1fffffff - 0x20000000 -1 = 2*16^7 - 1 = 536870912-1 =536870911

Since, each memory address holds a byte, then you'd be talking about a memory address from the 1st MB up to (just before) 512MB (given the convention that 1MB = 1048756 bytes)

Answer 2

\begin{array}{cc} & 0x &\ 1 &\ F &\ F &\ F &\ F &\ F &\ F &\ F \\ - &0x &\ 0 &\ 0 &\ 1 &\ 0 &\ 0 &\ 0 &\ 0 &\ 0 \\ + &0x &\ 0 &\ 0 &\ 0 &\ 0 &\ 0 &\ 0 &\ 0 &\ 1 \\ = &0x &\ 1 &\ F &\ F &\ 0 &\ 0 &\ 0 &\ 0 &\ 0 \\ \times & &\ 16^7 &\ 16^6 &\ 16^5 &\ 16^4 &\ 16^3 &\ 16^2 &\ 16^1 &\ 16^0 \\ \end{array}

Adding 1 goes from start to end.

$$1 \times 16^7 + 15 \times 16^6 + 15 \times 16^5 = 535,822,336\ bytes$$

0x100000 = 1MB = 1,048,576 bytes, so the address range from 0x00100000 to 0x1fffffff is 511MB.