The rules are the same as decimal. Only the carrying threshold changes. In decimal you carry at ten. In binary you carry at two.

Addition

Four rules only:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10  ← carry 1, write 0

Example: 1011 + 1101

  1011
+ 1101
------
 11000

Check: 11 + 13 = 24 → 11000 in binary ✓

Carry early, carry often. That’s all addition is in binary.

Subtraction

Four rules — mirror of addition:

0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1  ← borrow 1 from the left

Example: 1101 - 1011

  1101
- 1011
------
  0010

Check: 13 - 11 = 2 → 0010 in binary ✓

Borrowing in binary gives you 2, not 10 — because the base is 2.

Multiplication

Simpler than decimal — only two possible multipliers:

0 × anything = 0
1 × anything = that number

Multiply by each digit, shift left, add the partials.

Example: 101 × 11

    101
  ×  11
  -----
    101   ← 101 × 1
   1010   ← 101 × 1, shifted left
  ------
   1111

Check: 5 × 3 = 15 → 1111 in binary ✓

The Pattern

Same logic as decimal — different carry threshold.

Carry at 2, not 10. Borrow 2, not 10. Shift and add for multiplication.

Master these, and you understand what the CPU is doing at its most fundamental level — billions of times per second.