Binary: The Language of Machines

Every photo you've taken, every message you've sent, every model that's ever answered your question — all of it, at the bottom, is just two symbols: 0 and 1. This lesson explains why computers work this way, how a pile of bits becomes a number, and why this matters for AI.

The problem

We have ten fingers, so humans count in base 10: the number 342 means 3 hundreds + 4 tens + 2 ones. Each position is worth ten times the one to its right. But a machine with only two symbols can't have a "tens" place. So how do you write any number using only 0 and 1?

The answer: same trick, smaller base. In binary, each position is worth two times the one to its right. Instead of ones, tens, hundreds — you get ones, twos, fours, eights, sixteens...

How binary counting works

Take the binary number 1011. Reading right to left, the places are worth 1, 2, 4, 8:

place value:   8   4   2   1
digit:         1   0   1   1
contribution:  8 + 0 + 2 + 1  =  11

So 1011 in binary is 11 in decimal. Each digit is called a bit (binary digit). Going the other way — decimal to binary — you repeatedly ask "does the biggest power of 2 fit?":

Try it yourself

Play with the converter below. Suggestions: find the binary for your age. Notice what happens to a binary number when you double it (hint: same trick as multiplying by 10 in decimal). Find the largest number you can write with 8 bits.

If you experimented, you found that 8 bits max out at 11111111 = 255. Eight bits is called a byte, and it's the standard unit of computer memory. That's why so many limits in computing are 255 or 256, and why file sizes are measured in bytes.

A code example

Most languages can convert between bases in one line:

# Decimal to binary
bin(13)          # '0b1101'   (the 0b prefix just means "binary")

# Binary to decimal
int("1101", 2)   # 13

# How many values fit in a byte?
2 ** 8           # 256  (0 through 255)

Why AI engineers care

Everything a model touches is bits. The connection to AI is direct:

• Text must become numbers. The next lessons show how characters map to numbers (ASCII/Unicode) and then to bytes (UTF-8). Tokenizers — the front door of every LLM — often operate on those raw bytes.
• Model weights are numbers stored in bits. When you hear that a model was quantized from 16-bit to 4-bit numbers to run faster, that's literally about how many bits store each weight — fewer bits, less precision, smaller and faster model.
• Capacity and cost. Memory, bandwidth, and context are all budgeted in bytes. Intuition for bits is intuition for cost.

Build it yourself

Write a decimal-to-binary converter without using built-ins. The classic method: repeatedly divide by 2 and collect the remainders.

def to_binary(n):
    if n == 0:
        return "0"
    bits = ""
    while n > 0:
        bits = str(n % 2) + bits   # remainder becomes the next bit
        n = n // 2
    return bits

print(to_binary(13))   # should print 1101

Then extend it: write from_binary(s) that reverses the process, and verify from_binary(to_binary(n)) == n for a few values. Bonus: why does the remainder-collecting trick work? (Hint: dividing by 2 in binary shifts every digit right by one place.)

Summary

• Computers use binary because transistors are two-state switches — it's physics, not preference.
• Binary uses positional notation like decimal, but each place is a power of 2.
• n bits represent 2^n values; a byte (8 bits) holds 0–255 and is the basic unit of memory.
• Everything in AI — text, weights, context — is ultimately bits, and bit-width trade-offs (like quantization) are everyday engineering decisions.