Everything Is Bits: Binary, Hex, and the Limits of Representation

Hi, I'm Byte. Inside every computer there is really only one kind of thing: a switch that is either OFF or ON. We write OFF as 0 and ON as 1, and each switch is called a bit. Eight bits make a byte. That's it. Everything else — photos, songs, your homework — is just clever ways of arranging those 0s and 1s. Numbers come first. In our normal decimal system each place is worth ten times the one to its right. Binary works the same way but with two: places are worth 1, 2, 4, 8, 16, and so on. So 1011 means 8 + 0 + 2 + 1 = 11. Because long binary strings are hard for humans to read, we group bits and use hexadecimal (base 16), where digits run 0–9 then A–F. Four bits map to exactly one hex digit, so 1011 is hex B. Text uses an agreed code so every machine reads the same letters. ASCII gives each character a number (capital A is 65); Unicode extends this to cover emoji and every world script. Images are grids of pixels, and each pixel stores red, green, and blue brightness values, usually 0–255 each. Sound is captured by measuring the wave's height thousands of times per second — called sampling — and storing each measurement as a number. Here is the catch: representation is finite. With n bits you only get 2^n different values, full stop. Eight bits can count 0 to 255, no higher. Push past the top and you get overflow, where the number wraps around. Try to store a value like 1/3 and you must round it, creating tiny errors that can add up. Finite bits mean finite precision, and good programmers always plan for that limit. If you get stuck: for binary-to-decimal or hex conversion, write out the place values (8 4 2 1 for 4-bit; 128 64 32 16 8 4 2 1 for 8-bit) and mark which positions are ON. For hex digits above 9, remember A=10, B=11, C=12, D=13, E=14, F=15. For encoding questions, ask yourself what agreed-upon table maps symbols to numbers. For overflow or 2^n questions, count the bits and raise 2 to that power.