From Logic Gates to Systems: How Digital Computers Are Built

Motivation

Software often feels abstract, but every program ultimately runs on hardware built from simple components. This post explores how complex digital systems emerge from basic logic.

Digital Abstraction

Binary abstraction maps voltage ranges to logical values, trading precision for predictability.

Voltage
│  HIGH ─────────── 1
│  LOW  ─────────── 0
└─────────────────── Time

Combinational Logic

Combinational logic is stateless and depends only on current inputs.

A ──┐
    ├─ Logic ── OUT
B ──┘

Pseudocode:

OUT = f(A, B, C)

Sequential Logic

Adding memory introduces time and state.

Inputs → Logic → Next State
               ↓
             State (clocked)

Finite State Machines

FSMs model behavior using states and transitions.

[IDLE] → [ACTIVE] → [DONE]
   ↑                 ↓
   └─────────────────┘

Takeaway

Computers are layered systems where abstraction manages complexity.