Binary

Binary is a base-2 number system it uses exactly two digits: 0 and 1. The word comes from the Latin binarius, meaning “consisting of two.”

You already know the decimal system (base 10): digits 0-9, and each position is worth ten times the one to its right. Binary works the same way, but with only two digits and each position is worth twice the one to its right.

In decimal, when you run out of digits in a column you carry over to the next column (9 → 10). Binary works identically, but you carry after 1.

Notice that powers of 2 (1, 2, 4, 8, 16, …) always start with a 1 followed entirely by zeros just like powers of 10 do in decimal.

Binary → Decimal: Multiply each bit by its place value (a power of 2), then add all the results together.

Decimal → Binary: Repeatedly divide the number by 2. Each remainder (0 or 1) becomes a bit. Read the remainders from bottom to top.

Binary arithmetic follows the same rules as decimal arithmetic the only difference is that you carry after 1, not after 9.

This same addition logic is what happens inside your CPU billions of times per second. Every calculation your computer makes from rendering a pixel to running a machine-learning model ultimately reduces to binary arithmetic.

Numbers are straightforward to store in binary. But what about text? Computers handle this by assigning every character a number, then storing that number in binary.

ASCII (American Standard Code for Information Interchange) is one of the oldest character encodings. It maps 128 characters letters, digits, punctuation, spaces to integers 0-127. Each character only needs 7 bits, though computers typically use 8 bits (one byte) per character and leave the leading bit as 0.

Below is a message encoded entirely in binary. Use everything you've learned in this module conversions, place values, ASCII to decode it. Take your time; there are 11 characters.