Introduction
It is imperative to know the working of a computer from within for all students who are taking the subject computer science. The Computer System notes in Class 11 provide basic knowledge about the internal structure of a computer. This includes hardware, software, input/output devices, CPU, and different types of memories. They will also study operating systems, various software, Boolean algebra, numbering systems, and encoding techniques such as ASCII and Unicode. These notes on the computer system are highly detailed and have been created carefully with the aim of simplifying complex topics. The notes are very valuable to students, especially when they are preparing for exams. All students studying in class 11 in CBSE, ICSE, and other central and state boards can benefit from these notes.
Computer Systems and Organisation
This blog highlights three essential topics in computer science, namely Boolean Logic & Logic Gates, Number Systems and Conversion, and Encoding schemes. These topics serve as the building blocks for all advanced computer science topics.
1. Boolean Logic and Logic Gates
George Boole developed Boolean algebra in 1854. It operates on only two values: 1 (True) and 0 (False). All computing operations at the hardware level come down to Boolean operations. The logic gates represent the electronic hardware that implements the Boolean operations.
The Six Basic Logic Gates
- NOT – Inverts the input. 0 becomes 1, and 1 becomes 0.
- AND – Output is 1 only if ALL inputs are 1.
- OR – Output is 1 if AT LEAST ONE input is 1.
- NAND – Opposite of AND. Output is 0 only when all inputs are 1.
- NOR – Opposite of OR. Output is 1 only when all inputs are 0.
- XOR – Output is 1 when the inputs are DIFFERENT; 0 when they are the same.
Truth Tables
A truth table lists all possible input combinations and the corresponding output. It is the most reliable way to verify any Boolean expression.
NOT Gate
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
AND Gate
| A | B | A·B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR Gate
| A | B | A+B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NAND Gate
| A | B | NAND |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR Gate
| A | B | NOR |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
XOR Gate
| A | B | A⊕B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
De Morgan’s Laws
De Morgan’s Laws allow you to simplify Boolean expressions. They also prove that NAND and NOR are universal gates — you can build any other gate using only NAND, or only NOR.
- Law 1: ¬(A · B) = ¬A + ¬B → NOT(A AND B) = (NOT A) OR (NOT B)
- Law 2: ¬(A + B) = ¬A · ¬B → NOT(A OR B) = (NOT A) AND (NOT B)
2. Number Systems and Conversions
Computers process everything in binary (base-2). However, humans use decimal (base-10) daily. Computer scientists use four main number systems:
- Binary (Base 2) – Uses digits 0 and 1 only. Native language of computers. Example: 1010₂ = 10₁₀.
- Octal (Base 8) – Uses digits 0 to 7. Groups binary into sets of 3. Example: 12₈ = 1010₂.
- Decimal (Base 10) – Uses digits 0 to 9. Everyday human number system.
- Hexadecimal (Base 16) – Uses digits 0–9 and A–F. Groups binary into sets of 4. Example: FF₁₆ = 255₁₀.
Conversion Methods
| From | To | Method | Example |
|---|---|---|---|
| Decimal | Binary | Divide by 2 repeatedly; read remainders bottom to top | 13₁₀ → 1101₂ |
| Binary | Decimal | Multiply each bit by its place value (power of 2) and add | 1101₂ → 13₁₀ |
| Decimal | Octal | Divide by 8 repeatedly; read remainders bottom to top | 100₁₀ → 144₈ |
| Binary | Octal | Group binary digits into sets of 3 from right | 110 100₂ → 64₈ |
| Decimal | Hex | Divide by 16; map remainders ≥10 to letters A–F | 255₁₀ → FF₁₆ |
| Binary | Hex | Group binary digits into sets of 4 from right | 1111 1111₂ → FF₁₆ |
| Hex | Binary | Replace each hex digit with its 4-bit binary equivalent | A3₁₆ → 1010 0011₂ |
| Octal | Binary | Replace each octal digit with its 3-bit binary equivalent | 37₈ → 011 111₂ |
3. Encoding Schemes: ASCII, ISCII, and Unicode
Computers store everything as binary numbers, including text. An encoding scheme assigns a unique numeric code to each character so computers can store, process, and transmit text accurately. Without a common encoding standard, text from one computer would appear as garbled symbols on another.
Three Major Encoding Standards
- ASCII – American Standard Code for Information Interchange. Uses 7 bits to represent 128 characters: English letters, digits 0–9, punctuation, and control characters. Extended ASCII uses 8 bits for 256 characters. The letter ‘A’ = decimal 65.
- ISCII – Indian Script Code for Information Interchange. Developed by BIS in 1988. Designed for Indian scripts such as Devanagari, Bengali, Tamil, and Telugu. Uses 8 bits and is backward-compatible with ASCII for the first 128 code positions.
- Unicode – A universal standard that represents every character in every language. Currently defines over 1,40,000 characters. Available in formats including UTF-8 and UTF-32.
UTF-8 vs UTF-32
| Feature | UTF-8 | UTF-32 |
|---|---|---|
| Bits per character | Variable: 8 to 32 bits (1–4 bytes) | Fixed: 32 bits (4 bytes) always |
| ASCII compatibility | Yes — ASCII characters use only 1 byte | No direct compatibility |
| Storage efficiency | Highly efficient for English text | Less efficient — every character uses 4 bytes |
| Use case | Web pages, emails, APIs, modern software | Internal processing needing fixed-width simplicity |
| Example | ‘A’ = 1 byte (0x41) | ‘A’ = 4 bytes (0x00000041) |
Quick Knowledge Check
1. What is the decimal equivalent of the binary number 1011?
2. Which Boolean gate gives output 1 only when all inputs are 0?
3. Which encoding scheme was developed in India for Indian scripts?
Conclusion
In this post, we explored Boolean logic — the six logic gates, truth tables, De Morgan’s Laws, and universal gates. We then mastered all four number systems and their conversion methods, with binary as the universal bridge. Finally, we understood encoding schemes — ASCII for English, ISCII for Indian scripts, and Unicode/UTF-8 as the modern universal standard. These concepts form the foundation for all advanced topics in computer science.
Frequently Asked Questions
Boolean Logic and Logic Gates
What makes NAND and NOR “universal gates”?
NAND and NOR are called universal gates because you can construct any other logic gate — AND, OR, NOT, XOR — using only NAND gates, or alternatively using only NOR gates. This is extremely valuable in circuit manufacturing because a factory only needs to produce one type of gate to build any digital circuit.
Why do computers use binary instead of decimal?
Computers use binary because electronic circuits naturally operate with two states — ON (1) and OFF (0) — corresponding to high voltage and low voltage. Binary maps perfectly to the physical reality of transistors and logic gates.
Number Systems and Encoding
How is UTF-8 different from ASCII?
ASCII uses only 7 bits and represents 128 characters — primarily English letters, digits, and punctuation. UTF-8 uses a variable-width encoding of 1 to 4 bytes per character. Importantly, UTF-8 is fully backward-compatible with ASCII — the first 128 UTF-8 code points are identical to ASCII.
Why was ISCII developed when ASCII already existed?
ASCII was designed exclusively for the English language and could not represent Indian scripts like Devanagari, Bengali, or Tamil. The Bureau of Indian Standards (BIS) developed ISCII in 1988 specifically to support Indian languages using an 8-bit encoding. ISCII is backward-compatible with ASCII for the first 128 code points.
What is the decimal value of binary 1011?
Binary 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 8 + 0 + 2 + 1 = 11 in decimal. Each bit is multiplied by its place value (a power of 2, starting from the right at 2⁰), and all results are added together.