Evolution of Number Systems
Long before computers, civilisations invented their own ways to count and record numbers — each contributing an idea that shaped the mathematical foundation modern computing stands on.
| Number System | Time Period | Key Idea |
|---|---|---|
| Egyptian | 3000 BC | Decimal (base 10), pictographs for powers of ten |
| Sumerian / Babylonian | 2000 BC | Sexagesimal (base 60); space as placeholder for zero |
| Chinese | 1200 BC | Decimal (base 10); counting rods and boards |
| Greek (Ionian) | 500 BC | Letters of the alphabet; non-positional, no zero |
| Roman | 500 BC | Symbols I, V, X, L, C, D, M; non-positional, no zero |
| Mayan | 300 AD | Vigesimal (base 20); positional, with a symbol for zero |
| Hindu–Arabic | 5th–6th century AD | Positional decimal system; introduced the digit 0 (from India) |
The Hindu–Arabic system — positional, with zero — forms the basis of the modern number system used worldwide today.
Introduction to Computing Machines
Manual calculation was slow and error-prone — these are the milestone devices that made calculation faster and, eventually, programmable.
Abacus
Beads on rods for addition and multiplication using place value. Invented by the Mesopotamians, refined by the Chinese.
Napier's Bones
Numbered rods devised by John Napier for multiplication and division of any number by a single digit.
Pascaline
Blaise Pascal's gear-and-wheel adding machine — addition and subtraction with carry-transfer.
Leibniz's Calculator
Extended Pascal's machine to multiplication and division, done through repeated addition.
Jacquard's Loom
Punched cards controlled weaving patterns — a precursor to programmable computers.
Babbage's Engines
Difference Engine, then the Analytical Engine — with a processor, memory and I/O concept. Babbage: "Father of Computers."
Mark I
Howard Aiken & IBM's electromechanical computer — the first operational general-purpose computer.
Stored Program Concept
John von Neumann proposed storing program and data in the same memory unit — the basis of all modern computers.
Ada Lovelace
Worked with Babbage on the Analytical Engine and wrote the first algorithm intended for a machine — widely regarded as the first computer programmer. She was first to realise computers could create music, art and graphics, not just do mathematics.
Generations of Computers
Each generation is defined by a major hardware or software advancement that made computers smaller, faster and more capable.
| Generation | Dates | Technology |
|---|---|---|
| First | 1940–1956 | Vacuum Tubes — ENIAC, EDVAC, UNIVAC I |
| Second | 1956–1963 | Transistors — IBM 1401, IBM 1620; FORTRAN, COBOL |
| Third | 1964–1971 | Integrated Circuits (ICs) — IBM 360/370, PDP-8/11 |
| Fourth | 1971–Present | Microprocessors (LSI/VLSI) — Intel 4004, personal computers |
| Fifth | 1982–Present | Artificial Intelligence — ML, NLP, robotics, quantum & cloud computing |
2nd Gen Shift
Magnetic core memory enabled cost-effective long-term storage; commercial use in payroll & inventory took off.
3rd Gen Shift
OS with multitasking/multiprogramming (e.g. OS/360) — computers reached education and small business.
4th Gen Shift
Intel 4004 (1971) — the first microprocessor — enabled affordable, personal-use computers and the Internet.
Evolution of Programming Languages
From binary machine code to natural, English-like statements — languages evolved to reduce complexity and machine dependence.
Machine Language
Pure binary (0s, 1s). Directly understood by the CPU; fast but very hard to write, debug, and machine-dependent.
Assembly Language
Mnemonic codes like ADD, SUB, MOV instead of binary. Easier to write, but still machine-dependent.
High-Level Languages
English-like statements, machine-independent. Began with Short Code and Autocode; FORTRAN (1957) was the first widely used one.
Language Timeline
Programming paradigms: ■ Imperative — FORTRAN, COBOL, Pascal, C | ■ Object-oriented — C++, Java, Python, JavaScript | ■ Functional — LISP | ■ Logic — Prolog
How Computers Are Used & Data Processing
A functional computer needs both hardware and software. In practice, computers are used for four broad purposes:
Data Storage & Processing
DBMS, word processors, spreadsheets — e.g. the Aadhaar database storing information for crores of people.
Problem Solving
Designing algorithms and expressing them in languages like Python; compilers/interpreters and OS assist this.
Networking & Communication
The Internet connects computers for email, video calls, streaming and social media.
Intelligent Decision Making
Machine learning & AI — diagnosing disease, playing chess, self-driving cars, and IoT devices like smart bulbs.
Stages of Data Processing (in practice)
Input Format Design
Deciding structure in advance — a billing record layout, a registration form, an IoT sensor's units.
Data Input
Manual, automated or sensor-driven — barcode scans, web forms, IoT/AI camera feeds, VR controllers.
Data Storage
HDDs, SSDs, cloud storage and databases — for security, quick retrieval, and backup.
Data Processing
Validation, computation, comparison, decision-making — e.g. computing a Total Bill Amount.
Output & Visualisation
Reports, dashboards, alerts, charts, PDFs — presenting results clearly to the user.
Feedback Loop
IoT, AI cameras and game engines often feed fresh sensor/player data straight back into processing in real time.
Quick Recap
Tap a question to reveal the answer.
Which ancient number system was the first to use a symbol for zero, and which was positional with it?
The Mayan number system (300 AD) used a shell-shaped symbol for zero and was positional. The Hindu–Arabic system later combined a positional decimal system with the digit 0, contributed by India.
Why is Charles Babbage called the "Father of Computers"?
He designed the Difference Engine (1822) and the Analytical Engine (1833). The Analytical Engine included the concept of a central processor, memory storage, and input-output devices — establishing the basic principles modern computers work on, even though it was never built in his lifetime.
What was revolutionary about Jacquard's Loom?
It used punched cards to control weaving patterns automatically — the sets of punched holes acted like a program, making it a precursor to programmable computers.
What is the "stored program concept" and who proposed it?
John von Neumann (1945) proposed storing both the program and its data in the same memory unit — a major shift from earlier machines where instructions were fixed in hardware wiring or punched cards. All modern computers are based on this concept.
Which technology defines each generation of computers?
1st: Vacuum Tubes · 2nd: Transistors · 3rd: Integrated Circuits · 4th: Microprocessors · 5th: Artificial Intelligence.
Name the four main programming paradigms and give one example language of each.
Imperative/Procedural (FORTRAN, COBOL, Pascal, C), Object-oriented (C++, Java, Python, JavaScript), Functional (LISP), and Logic programming (Prolog).
Why was assembly language an improvement over machine language, and what limitation remained?
Assembly language used mnemonic codes (ADD, SUB, MOV) instead of raw binary, making programs easier to write and debug. However, it remained machine-dependent — a program written for one type of computer couldn't run on another without modification.