Hexadecimal Arithmetic

Hexadecimal Arithmetic (or Base-16 Math).It is the standard language of memory addressing in computer science.

Here is exactly how to do it step-by-step, just like you would with normal decimal numbers, but using 16 digits instead of 10.

The Basics: Base-16

In our normal world (Decimal), we count 0-9. In the computer world (Hex), we count 0-9 and then A-F.

• A = 10
• B = 11
• C = 12
• D = 13
• E = 14
• F = 15

---

Calculation 1: Finding the End of the Section

Problem: 0x13EA00 (Size) + 0x2000 (Start Address)

Stack them up like normal addition:

1 3 E A 0 0
+   2 0 0 0
---------------

1. Right to Left:

   • 0 + 0 = 0
   • 0 + 0 = 0
   • A + 0 = A

2. The Tricky Part:

   • E + 2
   • Remember: E is 14.
   • 14 + 2 = 16.
   • In Hex, 16 is written as 10 (just like how 'ten' is written as 10 in decimal).
   • So, write down 0 and carry the 1.

3. Finish it:

   • 3 + 1 (carry) = 4
   • 1 + 0 = 1

Result: 1 4 0 A 0 0 (or 0x140A00).

Calculation 2: Distance from the End

Problem: 0x140A00 (End) - 0x1409AA (Entry Point)

Stack them up for subtraction:

   1 4 0 A 0 0
-  1 4 0 9 A A
---------------

1. Right Column: 0 - A. You can't do 0 - 10. So you must borrow.
   • The neighbor is also 0, so borrow from the next neighbor (A).
   • This A becomes 9. The middle 0 becomes F (15), and the right 0 becomes 16 (in value).
   • Now: 16 - 10 (A) = 6.
2. Middle Column:
   • We have F (15) from the borrow.
   • 15 (F) - 10 (A) = 5.
3. Left Columns:
   • The A became 9 from the borrow. 9 - 9 = 0.
   • 0 - 0 = 0... and so on.

Result: 0x000056.

To convert 0x56 to decimal (normal numbers):

• Take the first digit (5) multiplied by 16: 5 * 16 = 80.
• Add the second digit (6): 80 + 6 = 86.

Answer: 86 bytes.

---

Pro Tip

You don't have to do this by hand! You can use Python right in your terminal:

# Calculate End Address
python3 -c "print(hex(0x2000 + 0x13ea00))"

# Calculate Distance
python3 -c "print(0x140a00 - 0x1409aa)"

# Convert Hex to Decimal
python3 -c "print(int('56', 16))"