Arithmetic Microprocessor

CSS Optional — Paper-II, Computer Organization & Architecture

1. Definition

The ALU (Arithmetic Logic Unit) is the combinational hardware block that carries out all arithmetic and logic operations required by an instruction.

2. Classification — ALU Operation Types

Arithmetic — addition, subtraction, multiplication, division, increment, decrement.
Logical — AND, OR, NOT, XOR.
Shift — left shift, right shift, rotate.

3. Classification — Multiplication Methods

Shift-add method — repeated shifting and conditional addition, mirroring long multiplication in binary.
Booth's algorithm — encodes runs of 1s to reduce the number of additions needed, especially efficient for signed numbers.

4. Subtraction via 2's Complement (high-yield)

A − B = A + (2's complement of B)

This lets the same adder circuit handle both addition and subtraction — the decisive reason 2's complement is used in every modern ALU.

5. Overflow Detection

Rule — overflow occurs only when adding two numbers of the same sign and getting a result of the opposite sign.
Adding a positive and a negative number can never cause overflow.

🗺️ Architecture Diagram — ALU Operation

graph LR
    A["Operand A"] --> ALU["ALU"]
    B["Operand B"] --> ALU
    OP["Operation Select
ADD / SUB / AND / OR / SHIFT"] --> ALU
    ALU --> R["Result"]
    ALU --> FLAGS["Status Flags
Z, C, S, V"]

🧮 Solved Numerical 1 — Binary Addition

Q: Add 0110 (6) and 0011 (3).

  0110
+ 0011
------
  1001

Answer: 1001 = 9.

🧮 Solved Numerical 2 — Subtraction via 2's Complement

Q: Compute 7 − 3 in 4-bit binary.

7 = 0111
3 = 0011  →  2's complement of 3 = 1101

  0111
+ 1101
-------
 10100   → drop the carry → 0100 = 4

Answer: 4.

🧮 Solved Numerical 3 — Overflow Check

Q: 4-bit addition: 0111 (+7) + 0001 (+1). Check for overflow.

  0111
+ 0001
------
  1000    (represents −8 in 2's complement)

Both operands were positive but the result is negative → overflow occurred.

Answer: Overflow = 1.

🎯 CSS Exam Angle

Binary arithmetic and overflow-detection numericals are frequently repeated compulsory-style questions.

🔁 Repeated CSS Questions

Perform binary subtraction using the 2's complement method with a worked example. (Numerical — very frequently repeated)
Explain overflow detection in binary addition with an example.
Briefly explain Booth's algorithm for binary multiplication.

⚠️ MCQ Trap

Overflow can only occur when adding two numbers of the same sign — adding a positive and a negative number can never cause overflow.