🧠 Introduction

A Binary Adder/Subtractor is a combinational circuit that can perform both addition and subtraction of two binary numbers using the same hardware.

👉 Instead of making two separate circuits (one adder and one subtractor), we design one smart circuit that can add or subtract based on a control input.

🎯 Purpose

To add two binary numbers OR
To subtract one binary number from another
using a single circuit.

⚙️ Working Principle

The circuit uses a Parallel Adder (multiple Full Adders).
It takes two binary numbers: A and B.
A control signal called Mode (M) decides the operation:
- If M = 0 → Perform Addition (A + B)
- If M = 1 → Perform Subtraction (A – B)

👉 Subtraction is done by using 2’s Complement Method:

Take 1’s complement of B (invert all bits of B)
Add 1 to it (carry-in becomes 1)

Thus, subtraction becomes:

A - B = A + (1's complement of B) + 1

🛠️ Circuit Structure

The circuit contains:

XOR gates to complement B when needed
Full Adders to perform the binary addition

📈 Block Diagram

Each bit has the following connection:

B[i] --|XOR|--- B'[i] ---> Full Adder
          |M|

A[i] ------------------> Full Adder
Cin ---- Carry In ---> Full Adder

Sum[i]  ---> Output
Carry Out --> Next Full Adder

XOR gate decides whether to invert B[i] or not.
Cin = M (control bit):
- M=0 → Add
- M=1 → Subtract

📑 Truth Table

Mode (M)	Operation	Action on B	Cin
0	A + B (Addition)	Use B as it is	0
1	A – B (Subtraction)	1’s complement of B	1

🧩 Detailed Working

For Addition (M = 0):

B[i] XOR 0 = B[i] → B remains unchanged
Cin = 0
Operation: A + B

For Subtraction (M = 1):

B[i] XOR 1 = ¬B[i] → B gets complemented (1’s complement)
Cin = 1
Operation: A + (1’s complement of B) + 1 (i.e., A – B)

🔥 Example: 4-bit Binary Adder/Subtractor

Suppose we have:

A = 0101 (5 in decimal)
B = 0011 (3 in decimal)

👉 Addition (M=0):

  0101 (A)
+ 0011 (B)
---------
  1000 (8)

👉 Subtraction (M=1):

1’s complement of B = 1100
Add Cin = 1

 0101 (A)
+ 1100 (¬B)
+    1 (Cin)
---------
  0010 (2)

Thus, 5 – 3 = 2 ✅

🧠 Important Components

Component	Function
XOR Gate	Complements B bits based on Mode M
Full Adder	Performs addition of A, modified B, and Carry In
Control Signal (M)	Decides Addition or Subtraction

🌟 Advantages of Binary Adder/Subtractor

Single circuit can perform two operations (saving hardware cost).
Fast — just by changing Mode (M) signal.
Simple design — only need XOR gates + Full Adders.

⚡ Applications

Arithmetic Logic Units (ALUs) inside CPUs
Digital calculators
Microprocessors and Microcontrollers
Digital systems that require fast arithmetic operations

🎯 Summary

Feature	Binary Adder/Subtractor
Operations	Addition or Subtraction
Controlled by	Mode (M)
Hardware	XOR Gates + Full Adders
Addition Method	Direct addition
Subtraction Method	2’s complement (invert B + add 1)
Major Use	In ALUs, CPUs, Digital Devices

✏️ Pro Tip for Exams

Always draw the Block Diagram with XOR gates and Full Adders.
Explain the working separately for M=0 and M=1 cases.
Use simple examples like 4-bit addition/subtraction to show clarity.