Behind every click, tap, and screen you interact with — lies a world of numbers, logic, and codes. This post will introduce you to the foundation of digital electronics and computing: Number Systems, Boolean Logic, and Encoding Schemes.
🔹 Number Systems in Computers
Computers can’t understand words — they process everything as numbers. Let’s look at the four major number systems:
| Number System | Base | Digits Used | Example |
|---|---|---|---|
| Binary | 2 | 0, 1 | 10102 |
| Octal | 8 | 0–7 | 758 |
| Decimal | 10 | 0–9 | 5910 |
| Hexadecimal | 16 | 0–9, A–F | 3F16 |
🔄 Conversions Between Number Systems
- Binary to Decimal: Multiply each bit by 2n and sum them.
- Decimal to Binary: Divide the number by 2 repeatedly and write remainders in reverse.
- Similar steps are used for Octal and Hex conversions.
🔹 Boolean Logic and Gates
Computers make decisions using logic gates, which operate on binary inputs (0 and 1). These are the core of all digital circuits.
🔌 Basic Logic Gates
- AND Gate: Output is 1 only if both inputs are 1
- OR Gate: Output is 1 if at least one input is 1
- NOT Gate: Inverts the input
🔐 Advanced Logic Gates
- NAND Gate: NOT of AND
- NOR Gate: NOT of OR
- XOR Gate: Output is 1 if inputs are different
🧠 Truth Tables
| A | B | AND | OR | XOR |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 |
📘 De Morgan’s Laws
These are two important laws used in Boolean simplification:
- ¬(A ∧ B) = ¬A ∨ ¬B
- ¬(A ∨ B) = ¬A ∧ ¬B
🔹 Encoding Schemes
Encoding schemes are used to represent characters and symbols as binary values.
🅰️ ASCII (American Standard Code for Information Interchange)
- Uses 7 or 8 bits
- Example: A = 65, a = 97
🇮🇳 ISCII (Indian Script Code for Information Interchange)
- Developed for Indian languages
- Supports scripts like Devanagari, Tamil, etc.
🌐 Unicode
- Universal encoding standard
- UTF-8: Variable length, efficient for English
- UTF-32: Fixed 4 bytes per character, simpler for computation
📝 Summary
- Number systems are the foundation of computer arithmetic.
- Logic gates and Boolean algebra power decision-making in machines.
- Encoding schemes represent text using binary numbers.
📘 Explore Previous Blogs
💡 Tip: Practice conversions and logic gate tables regularly to sharpen your digital reasoning skills!
Congratulations! You’ve now completed Unit I of Class XI Computer Science. 🚀