How a computer runs a program

Binary and hexadecimal

Also called base 2, base 16, hex, hexadecimal

What

Number systems with base 2 and base 16. Each hex digit stands for exactly four bits, so hex is a compact way to write binary values.

Why

Memory addresses, colours, permissions, packet dumps and bit flags are all written in binary or hex. Converting by hand builds the intuition to read them.

Example

Decimal 202 is binary 1100 1010, which is hex CA: 1100 is C and 1010 is A.

Two's complement

What

The standard way to store signed integers: to negate a number, invert every bit and add one. The top bit acts as the sign.

Why

It lets the same adder circuit handle positive and negative numbers, and it explains why signed values wrap from the maximum to the minimum on overflow.

  5  = 0000 0101
 invert 1111 1010
  + 1 = 1111 1011  = -5

 8-bit range: -128 to 127
 127 + 1 wraps to -128

Character encoding

Also called ASCII, Unicode, UTF-8

What

The mapping from characters to numbers and bytes. Unicode gives every character a code point; UTF-8 stores each code point in one to four bytes, keeping ASCII as one byte.

Why

Every string, file and database column has an encoding. Getting it wrong produces garbled text and broken length checks for any language beyond English.

Example

The letter A is one byte in UTF-8, the Urdu letter ب is two bytes, and most emoji are four.

Floating point

Also called IEEE 754, float, double

What

The binary format for real numbers: a sign, an exponent and a fraction. Most decimal fractions, such as 0.1, cannot be stored exactly.

Why

It explains rounding surprises and why money is stored as integer cents or a decimal type, and why floats are compared with a small tolerance.

>>> 0.1 + 0.2
0.30000000000000004
>>> 0.1 + 0.2 == 0.3
False
>>> abs((0.1 + 0.2) - 0.3) < 1e-9
True

Logic gates

Also called AND, OR, NOT, NAND, XOR

What

Tiny circuits that compute a boolean function of their inputs. Every other digital circuit, from adders to memory, is built by combining them.

Why

They show that a computer is layers of simple parts. A half adder, for example, is one XOR gate for the sum and one AND gate for the carry.

CPU, registers and ALU

Also called processor, arithmetic logic unit, program counter, CPU, ALU, register

What

The CPU executes instructions. Registers are its few, very fast storage slots; the ALU does arithmetic and logic; the control unit steers each step; the program counter holds the next instruction address.

Why

Knowing these parts lets you read assembly, understand what a context switch saves, and see why keeping data in registers and caches is fast.

Fetch, decode, execute

Also called instruction cycle, fetch-decode-execute cycle

What

The loop every CPU runs: fetch the instruction at the program counter, decode it, execute it, then move to the next instruction or jump.

Why

High-level code compiles into long sequences of these simple steps, which is why one line of code can take many instructions.

loop:  LOAD  R1, [i]
       ADD   R2, R2, R1
       ADD   R1, R1, 1
       STORE [i], R1
       CMP   R1, 10
       JLE   loop

Memory hierarchy

Also called cache, locality, L1, L2, L3

What

Storage layers from registers and CPU caches to RAM, SSD and network, each much larger and much slower than the one above.

Why

Caches work because of locality: programs reuse recent data and read nearby addresses. Code that respects this, such as scanning arrays in order, runs much faster.

Example

Rough latencies: register under 1 ns, L1 cache about 1 ns, RAM about 100 ns, SSD read about 100 microseconds, a cross-continent round trip about 150 ms.

Stack and heap

Also called stack frame, stack overflow, call stack

What

Two memory regions of a running program. The stack holds call frames with locals and return addresses; the heap holds data allocated at run time with a flexible lifetime.

Why

It explains stack overflows from deep recursion, memory leaks, dangling pointers, and what a garbage collector actually manages.

Compiler, interpreter and JIT

Also called bytecode, virtual machine, JVM, JIT, just-in-time compiler, Java virtual machine

What

A compiler translates a whole program to machine code ahead of time; an interpreter executes it as it reads. Many languages compile to bytecode run by a virtual machine with a just-in-time compiler.

Why

It decides when errors appear, how fast code starts and runs, and what must be installed to run the program.