What is binary?

Why computers speak in 0s and 1s

You count using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This is the decimal system (base-10), and you use it because you have ten fingers.

Computers do not have fingers. They have transistors, tiny electronic switches. A computer's circuits treat each one as either on or off. There is no "half-on" or "sort of off" as far as the logic is concerned. Just two states.

Because of this physical limitation, computers use the binary system (base-2), which has only two digits: 0 and 1.

Transistor OFF = 0
Transistor ON  = 1

Every number, every letter, every pixel of every image, every byte of every Ruby file: all of it is ultimately stored as a sequence of 0s and 1s inside your computer.

Counting in binary

In decimal, when you run out of digits (after 9), you add a new column to the left and reset:

 8,  9, 10, 11, 12, ...

Binary works the same way, but you run out of digits after 1:

Decimal:  0   1   2   3   4   5   6   7   8
Binary:   0   1  10  11 100 101 110 111 1000

Let us break down how binary columns work:

Decimal columns (base-10):
  1000s  100s  10s  1s
    1      2    5    3   = 1×1000 + 2×100 + 5×10 + 3×1 = 1253

Binary columns (base-2):
  128s  64s  32s  16s  8s  4s  2s  1s
    1    0    0    1   1   0   1   0  = 128+16+8+2 = 154

Each column in binary is a power of 2 (1, 2, 4, 8, 16, 32, 64, 128...), just like each column in decimal is a power of 10.

The powers of 2: a developer's best friend

These numbers will appear everywhere in your career:

When a database column is integer (32-bit signed), its maximum value is 2³¹ - 1 = 2,147,483,647. Past that, you need bigint (64-bit). Rails has created bigint primary keys by default since Rails 5.1, so this limit mostly bites older tables and plain integer columns.

Binary in Ruby

Ruby lets you write numbers directly in binary using the 0b prefix:

0b1010        # => 10
0b11111111    # => 255
0b10000000    # => 128

You can also convert between decimal and binary:

# Decimal to binary string
42.to_s(2)       # => "101010"
255.to_s(2)      # => "11111111"

# Binary string to decimal
"101010".to_i(2) # => 42
"11111111".to_i(2) # => 255

Binary shows up in daily work. You will use binary operations when working with:

• File permissions (chmod 755 is binary flags)
• Bitwise flags (feature toggles stored as a single integer)
• Network masks (IP subnets use binary AND operations)
• Color values (RGB channels packed into integers)

Converting decimal to binary by hand

To convert a decimal number to binary, repeatedly divide by 2 and collect the remainders:

42 ÷ 2 = 21 remainder 0  ─┐
21 ÷ 2 = 10 remainder 1   │
10 ÷ 2 =  5 remainder 0   │  Read remainders
 5 ÷ 2 =  2 remainder 1   │  BOTTOM to TOP:
 2 ÷ 2 =  1 remainder 0   │  101010
 1 ÷ 2 =  0 remainder 1  ─┘

42 in decimal = 101010 in binary ✓

Verification: 1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1 = 32 + 8 + 2 = 42 ✓

Why this matters for Rails developers

You might wonder: "I write Ruby, not binary. Why should I care?"

1. Database IDs: When an integer id column reaches 2,147,483,647 (2³¹ - 1), inserts fail. This app's users.id is a bigint, so it won't. Understanding binary tells you why and when.

2. Character encoding: A UTF-8 emoji like 😀 takes 4 bytes (32 bits). PostgreSQL's varchar(1) counts characters, so the emoji fits, but it still occupies 4 bytes. Any limit measured in bytes sees "1 character" ≠ "1 byte".

3. Permissions: chmod 755 means 111 101 101 in binary: owner can read/write/execute, group and others can read/execute.

4. Performance: Bitwise operations (&, |, ^, <<, >>) are among the fastest operations a CPU can perform, usually a single clock cycle at the hardware level.

Summary