Binary Numbers

Binary is the number system that computers use internally. While humans use decimal (base 10), computers use binary (base 2).

Understanding binary is essential for Assembly programming because you're working directly with how the CPU stores and processes data.

Comparing Decimal and Binary

Let's look at how we count in decimal vs. binary:

Decimal  |  Binary
---------|---------
   0     |    0
   1     |    1
   2     |   10
   3     |   11
   4     |  100
   5     |  101
   6     |  110
   7     |  111
   8     | 1000
   9     | 1001
  10     | 1010

Notice how binary needs more digits to represent the same number? That's because it only has 2 digits available instead of 10.

How Binary Works: Place Values

In decimal, each position represents a power of 10:

Number: 3 4 5
         ↓ ↓ ↓
       100 10 1
       (10²)(10¹)(10⁰)

So 345 = (3 × 100) + (4 × 10) + (5 × 1) = 345

In binary, each position represents a power of 2:

Number: 1 0 1
        ↓ ↓ ↓
        4 2 1
       (2²)(2¹)(2⁰)

So 101 = (1 × 4) + (0 × 2) + (1 × 1) = 5 in decimal

Understanding binary is fundamental because when you start writing Assembly code, you'll be working directly with how the CPU sees data - as binary values stored in registers and memory.