---
Computers are everywhere—from your smartphone to the most advanced AI systems. But beneath all the code, apps, and interfaces lies something simple yet powerful: math. At the core of every computer is a system built on binary numbers, bits, and logic gates.
In this post, we’ll explore the fascinating math that makes computers tick.
---
🔢 1. What Is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1.
Unlike the decimal system (base-10), which uses digits from 0 to 9, binary is all about two states:
0 → OFF / Low Voltage
1 → ON / High Voltage
Computers use binary because digital circuits can easily detect these two states using electrical signals.
Example:
The decimal number 5 in binary is 101.
That’s because: 1×2² + 0×2¹ + 1×2⁰ = 4 + 0 + 1 = 5
---
🧩 2. What’s a Bit?
A bit is short for binary digit—the smallest unit of data in a computer.
Just like a letter in a word, bits are the building blocks of all digital data:
1 bit = 0 or 1
8 bits = 1 byte (enough to store a single letter like "A")
1024 bytes = 1 kilobyte (KB), and so on…
A typical image or video contains millions or billions of bits!
---
🧠 3. How Computers Use Logic (Boolean Algebra)
Behind every program or app is logic—and that’s where Boolean Algebra comes in. It’s a system of math with only two values: True (1) and False (0).
Computers use logic gates to make decisions. These gates are basic circuits that follow Boolean rules.
🔀 Examples of Logic Gates:
AND Gate – Output is 1 only if both inputs are 1
1 AND 1 → 1, otherwise → 0
OR Gate – Output is 1 if at least one input is 1
NOT Gate – Flips the input: 1 → 0, 0 → 1
These gates are combined to build complex circuits—from calculators to CPUs.
---
🔄 4. Math in Memory & Processing
🧮 Numbers:
All kinds of numbers—integers, decimals, negative values—are stored using binary. Computers use systems like:
Unsigned Binary for only positive numbers
Two’s Complement to represent negative numbers
🧠 Instructions:
The processor (CPU) follows binary instructions, called machine code, to perform operations like add, move, compare, jump, etc.
All of this is based on binary math!
---
📱 5. Real-Life Example: What Happens When You Press a Key?
Let’s say you press the key “A” on your keyboard:
1. Your keyboard sends the binary code 01000001 (ASCII for ‘A’)
2. The processor receives that as 8 bits
3. Logic circuits inside your CPU route and process the signal
4. Your display shows “A” on the screen
From binary to logic to output—it’s all math at work.
---
🚀 Conclusion: Why It Matters
Understanding binary and logic helps you:
Grasp how software connects to hardware
Build better programs, circuits, or AI models
Appreciate the simplicity and elegance of how computers "think"
> 🎯 Fun Fact: The first ever digital computer (ENIAC) used vacuum tubes to represent 0s and 1s. Today, your phone does it with billions of tiny transistors!
---
0 Comments