HG

Multiplication and Division Instructions in Integer Arithmetic

Class Overview

  • Focus on multiplication and division operations in integer arithmetic.
  • Fast division and multiplication techniques using shift operations were previously covered.
  • Today: Detailed discussion on multiplication, potential division coverage depending on time.

Teaching Context

  • Acknowledgment of challenges faced by students (work, stress) amid current circumstances.
  • Emphasis on collaboration and support throughout the semester.

Multiplication Basics

  • Terminology:
  • Multiplicand: The number being multiplied (e.g., 4 in 4 x 5).
  • Multiplier: The number by which another number is multiplied (e.g., 5 in 4 x 5).
  • Product: The result of multiplication (e.g., 20 in 4 x 5).
  • Instructions for Multiplication:
  • mall instruction for unsigned integers.
  • imal instruction for signed integers.
  • Division instructions:
  • div for unsigned integers, idiv for signed integers.

Functionality of mall Instruction

  • Default operand (multiplicand) location in registers (AL, AX, EAX) determined by the operand size:
  • 8-bit: AL
  • 16-bit: AX
  • 32-bit: EAX
  • Only one operand required for mall, which must be a register or memory (not immediate).
  • Result stored in AX or extended register (if overflow).
  • Concatenated results for larger products (e.g., EAX and EDX for 32-bit).
  • Carry flag: signifies significant value in extended registers, helping avoid unnecessary reads of the entire register.

Examples of mall Usage

  • Multiplying two numbers, such as:
  • Move multiplicand (e.g., 4) to AL.
  • Move multiplier (e.g., 5) to BL.
  • Execute multiplication: mall BL.
  • Result resides in AX with considerations for overflow.

Factorial Example

  • Using loops to calculate factorials, e.g., 5!.
  • The process involves iterative multiplication using the mall instruction:
  • Assign number to the loop counter (CX), assign 1 to AX as starting multiplicand.
  • Iteratively update AX with the product of the current CX value until reaching zero.

Transition to imal Instruction

  • Focus shift from mall to imal, which handles signed integers.
  • Important differences when using imal:
  • Sign extension requirements for negative results.
  • Multiple variations of operand count (one, two, or three operands).
  • Overflow handling is crucial as the result may exceed the designated range for signed integers.

Detailed Differences Between mall and imal

  • mall:
  • Primarily for unsigned multiplication.
  • Can only take one operand.
  • The output is automatically managed in specific registers based on size.
  • imal:
  • Adapts for signed numbers, interpreting the sign crucially.
  • Can take one, two, or three operands.
  • Adjusts for truncation issues—if the destination cannot hold the result, an overflow flag indicates the need for further evaluation.

Summary and Next Steps

  • Encourage practice with examples during lab sessions.
  • Remind students of upcoming topics (division in the next class).
  • Open invitation to office hours for additional support.