➕ Basics of Digital Logic (Arithmetic Operations)
Think about how we do math every day — adding groceries’ prices, counting steps, or subtracting expenses.
Computers do the same kind of math, but instead of using our decimal numbers, they use binary digits — just 0s and 1s.
The process of performing mathematical calculations using binary numbers is what we call Arithmetic Operations in Digital Logic.
💡 What Are Arithmetic Operations?
Arithmetic operations are basic mathematical functions — addition, subtraction, multiplication, and division.
In digital systems, all these operations are done using binary arithmetic, where numbers are represented in base 2 (only 0 and 1).
Before we go into each, remember one simple rule:
Every calculation that we can do on paper, a computer can do too — it just follows binary versions of our familiar rules.
🔹 1. Binary Addition
Binary addition is just like decimal addition, except there are only two digits to work with.
Let’s see the four possible cases:
| A | B | Sum | Carry |
| – | – | — | —– |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
So, 1 + 1 = 10 in binary (that’s 2 in decimal).
Example:
1011
+ 1101
-------
11000That’s 24 in decimal.
In circuits, this operation is performed using logic gates — specifically by adders (Half Adder and Full Adder).
🔹 2. Binary Subtraction
Binary subtraction is also similar to decimal subtraction, but we use borrowing instead of carrying.
Here are the basic rules:
| A | B | Difference | Borrow |
| – | – | ———- | —— |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 |
Example:
1011
- 1001
--------
0010That’s 2 in decimal.
Digital circuits perform this using Subtractors (Half Subtractor and Full Subtractor).
🔹 3. Using Complements for Subtraction
Another clever way computers handle subtraction is through complements, especially the 2’s complement method.
Here’s the trick:
To subtract B from A,
- Find the 2’s complement of B (which means invert all bits and add 1).
- Add it to A.
- Ignore the carry if it appears.
This method helps computers perform subtraction using addition circuits only, making hardware simpler and faster.
🔹 4. Binary Multiplication
Binary multiplication works just like normal multiplication, but again, with 0s and 1s.
| A | B | Product |
| – | – | ——- |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Example:
101
× 11
--------
101 (101 × 1)
+ 1010 (101 × 1, shifted left)
--------
1111That’s 15 in decimal.
Computers perform this through sequential addition of shifted binary numbers — kind of like how we multiply by hand.
🔹 5. Binary Division
Binary division is just repeated subtraction, similar to decimal long division.
Example:
Divide (1010)₂ by (10)₂
→ (10)₂ fits in (1010)₂ exactly (101)₂ times.
That’s 5 in decimal, which checks out because 10 ÷ 2 = 5.
Division in computers uses circuits called dividers or is handled through software algorithms.
🧠 Real-Life Analogy
Imagine teaching a robot how to do math.
You show it how to add, subtract, multiply, and divide — but you can only say “yes” (1) or “no” (0).
That’s exactly what digital logic does!
It trains circuits to perform calculations using those two simple signals.
⚙️ Where It’s Used
Arithmetic operations form the core of the ALU (Arithmetic Logic Unit) in every processor.
This part of the CPU handles all math and logic — from calculating your phone’s battery percentage to performing complex scientific computations.
- Arithmetic operations in digital logic mean performing math using binary numbers.
- The main operations are addition, subtraction, multiplication, and division.
- Circuits like adders, subtractors, and ALUs make these operations happen in hardware.
- Using complements, computers can simplify subtraction into addition tasks.
- These simple binary steps power every complex calculation your computer performs.
About the Author
