Everything Is a Number

EVERYTHING IS A NUMBER How Computers Work · 01 — bits, bytes, and how ONE pattern of switches becomes text, numbers & colour a computer knows exactly ONE trick: a switch that is ON or OFF. that's a BIT (1 or 0). stack eight of them = a BYTE. everything above is just bytes, INTERPRETED. 1 · A BIT, THEN A BYTE a BIT = one switch (a transistor): 1 = on / high voltage, 0 = off / low. that's the whole alphabet. line up 8 bits = 1 BYTE = 256 possible patterns (0 – 255). each slot has a PLACE VALUE: 128 0 64 1 32 0 16 0 8 0 4 0 2 0 1 1 add the ON columns: 64 + 1 = 65 so the byte 01000001 is the number 65. binary is just base-2 with the same place-value idea as base-10. why 8? it's the smallest chunk the machine addresses as a unit — the atom of memory. (a WORD = a few bytes, later.) counting in binary: 0, 1, 10, 11, 100, 101, 110, 111, 1000 ... (each new digit = double the range). 0000=0 0001=1 0010=2 0011=3 0100=4 0101=5 0110=6 0111=7 1000=8 2 · HEX — the human shorthand for bytes binary is long to read. group 4 bits = a NIBBLE = ONE hexadecimal digit (base 16, 0–F). so 2 hex digits = exactly 1 byte. this is why hex is everywhere. 0100 0001 4 1 → 0x41 = 65 the hex digits past 9: A=10 B=11 C=12 D=13 E=14 F=15 you already read hex every day: · colours (#1E1E1E) · memory addresses (0x7ffe...) · byte dumps, hashes, MAC addresses, UUIDs 1 byte = 2 hex = 8 bits = 0 to 255 = 0x00 to 0xFF. burn that chain in. 3 · THE BIG IDEA: one byte, many meanings the bits don't KNOW what they are. meaning is imposed by the TYPE — the agreement on how to read them. 0100 0001 the very same byte can be... · the NUMBER 65 · the letter 'A' (ASCII: A=65, a=97, '0'=48) · one channel of a colour · a CPU instruction, a pixel, a flag... "there is no text or number 'on the wire' — only bytes plus an agreement on how to interpret them." (exactly the lesson from the DNS telegram & DDIA encoding — this is where it bottoms out.) TEXT ASCII = 1 byte per character (English). UNICODE / UTF-8 = 1–4 bytes (é, 中, 😀) so the whole world's writing fits. COLOUR RGB = one byte each for Red, Green, Blue. #1E1E1E = (30, 30, 30) #1971C2 = this board's blue ...so a file is just bytes + a rule. a .txt says 'read me as ASCII'. a .png says 'read me as pixels'. a .mp3 says 'read me as sound'. the file EXTENSION / header is that agreement, nothing more. rename .png to .txt and the bytes don't change — only how you READ them. 4 · HOW BIG, AND WHICH WAY ROUND WORD SIZE — how many bits the CPU grabs at once: 32-bit vs 64-bit. it also sets the ADDRESS SPACE: 32-bit can address ~4 GB of RAM; 64-bit addresses ~16 exabytes. that's the real reason your machine is '64-bit'. ENDIANNESS — byte order of a multi-byte number: · BIG-endian: most-significant byte first (human order). it's 'network byte order' — callback to Networking! · LITTLE-endian: least-significant first (x86 / your laptop). 0x12345678 -> BE: 12 34 56 78 LE: 78 56 34 12 UNITS (and a classic gotcha): · bit = b · byte = B (8 bits) · KB, MB, GB, TB (×1000) vs KiB, MiB (×1024) your '100 Mbps' internet is mega-BITS/s → ÷8 ≈ 12.5 MB/s of actual download. bits vs bytes bites everyone. JARGON, DECODED bit = one 0/1 switch · byte = 8 bits (0–255) · binary = base 2 · hexadecimal = base 16 (0–F), 1 hex digit = 4 bits (a nibble), 2 hex = 1 byte ASCII = 1-byte character code (A=65) · Unicode / UTF-8 = variable-length code for all writing · RGB = red/green/blue, one byte each · type = the agreement on how to read bytes word size = bits the CPU handles at once (32/64-bit) → also the address space · endianness = byte order of a multi-byte value (big = network order, little = x86) bit (b) vs byte (B) — network speeds are in bits! · KB (×1000) vs KiB (×1024) · nibble = 4 bits · the whole chain: 1 byte = 2 hex = 8 bits = 0–255 = 0x00–0xFF