L-1.9: Arithmetic Instructions(Data Manipulation) in Computer Organisation and Architecture

Summary

In this educational video, the host delves into the realm of arithmetic instructions in computing, explaining how basic operations like addition, subtraction, multiplication, and division are executed by a computer's hardware, specifically the CPU. The discussion highlights the importance of hardware support for these operations for efficiency and touches on how they can be implemented in programming languages like C. The video also explores the concept of increment and decrement operations, the role of the ALU, and the nuances of instructions versus micro-operations. It concludes with insights on how these instructions vary based on data types and addressing modes, providing a foundational understanding of computer arithmetic.

Takeaways

• 📚 Arithmetic instructions are essential for data manipulation in programming languages, involving operations like addition, subtraction, multiplication, and division.
• 🔄 Basic computers, regardless of size, include hardware support for at least addition and subtraction, which can be used to perform more complex operations like multiplication and division through looping.
• 💻 Modern commercial systems typically have dedicated hardware for all four basic arithmetic operations, ensuring efficiency and optimized performance.
• 🔩 The Arithmetic Logic Unit (ALU) in computers is responsible for performing arithmetic operations, including the four basic ones mentioned above.
• 🔄 Increment and decrement operations are used to adjust values in registers, often implemented as counters that can be easily increased or decreased with each clock pulse.
• 📝 The difference between an instruction and a micro-operation is that an instruction is a high-level command, while micro-operations are the low-level steps the processor follows to execute the instruction.
• 🔢 Addressing modes, such as immediate, direct, or indirect, determine how operands are accessed during arithmetic operations, with each mode having its specific use case and implementation.
• 🔑 The execution of arithmetic instructions involves several steps, including instruction fetch, decode, operand location determination, and execution of micro-operations.
• 🔄 Carry and borrow are concepts used in arithmetic to handle overflow in addition and underflow in subtraction, respectively, and are managed by specific instructions.
• 🔀 The NEGATE instruction is used to represent a number in its negative form, often implemented through the 2's complement method in computer systems.
• 🌐 Variations in arithmetic instructions depend on factors like the type of data being processed (integers or floating-point numbers) and the addressing mode used, leading to a flexible set of instructions tailored to different computing needs.

Q & A

What are arithmetic instructions in the context of data manipulation?

Arithmetic instructions are a type of data manipulation instruction that includes operations like addition, subtraction, multiplication, and division, which are fundamental to programming languages and are performed by the computer's hardware, specifically the CPU.

How can multiplication be achieved using addition?

Multiplication can be achieved using addition by repeatedly adding a number to itself a certain number of times. For example, to calculate 2*3, one would add the number 2 three times.

What is the role of the ALU in performing arithmetic operations?

The Arithmetic Logic Unit (ALU) is responsible for performing arithmetic operations such as addition, subtraction, multiplication, and division. It is a crucial component of the CPU that handles the computation tasks.

How does the CPU perform division using subtraction?

Division can be performed using subtraction by repeatedly subtracting the divisor from the dividend until the result is less than the divisor, keeping track of the number of subtractions to determine the quotient.

What is the significance of having hardware support for arithmetic operations?

Having hardware support for arithmetic operations ensures efficiency and optimized performance. Without dedicated hardware, these operations would have to be performed through software loops, which would be less efficient.

What is the difference between an instruction and a micro-operation?

An instruction is a high-level command that the CPU executes, while a micro-operation is a low-level, internal step that the hardware takes to fulfill the instruction. Instructions are composed of multiple micro-operations.

Can you explain the concept of increment and decrement in registers?

Increment and decrement are operations that adjust the value in a register by one. Increment increases the value by one, while decrement reduces it by one. These operations are often used for counting or adjusting values in loops or counters.

What is the purpose of the 'add with carry' instruction?

The 'add with carry' instruction is used when performing addition that may result in a carry, which is a value that needs to be added to the next higher bit. This instruction ensures that the carry is properly accounted for in the final result.

How is the 'subtraction with borrow' operation different from regular subtraction?

The 'subtraction with borrow' operation is used when the subtrahend is larger than the minuend, and it involves borrowing from the next higher bit to complete the subtraction. This operation keeps track of the borrow for use in subsequent calculations.

What does the NEGATE instruction do, and how is it used?

The NEGATE instruction is used to change the sign of a number, effectively converting it to its negative form. It is often implemented through the 2's complement method, which is a way to represent negative numbers in binary.

How do addressing modes affect the complexity of arithmetic instructions?

Addressing modes determine how operands are accessed in memory, and they can affect the complexity of arithmetic instructions. Different addressing modes, such as immediate, direct, or indirect, require different handling by the CPU, which can influence the efficiency and the number of micro-operations needed.

Outlines

00:00

💻 Arithmetic Instructions in Computing

This paragraph introduces the concept of arithmetic instructions in computing, focusing on how basic arithmetic operations like addition, subtraction, multiplication, and division are implemented in programming languages and hardware. It explains that even the simplest computers have the capability to perform addition and subtraction, which can be used to perform more complex operations like multiplication and division through looping. The paragraph also touches on the efficiency of these operations when hardware support is available, contrasting it with the need for software emulation in the absence of such hardware. The Arithmetic Logic Unit (ALU) is mentioned as the component that performs these operations, and the paragraph sets the stage for a deeper dive into how these operations are executed at the hardware level.

05:01

🔍 Deep Dive into Arithmetic Operations and Micro-Operations

The second paragraph delves deeper into the mechanics of arithmetic operations, discussing the role of increment and decrement operations and their application in registers. It explains how these operations are used to create counters that can be incremented or decremented with each clock pulse. The paragraph also clarifies the difference between instructions and micro-operations, emphasizing that an instruction like addition involves multiple internal steps within the ALU or processor. It introduces the concept of addressing modes and how they affect the execution of arithmetic operations, including immediate, direct, and indirect addressing. The paragraph concludes with a discussion on how the type of data (integers or floating-point numbers) and the hardware capabilities influence the choice and execution of arithmetic instructions, including variations like add with carry and subtract with borrow. The concept of the NEGATE operation, used to represent numbers in their negative form, is also briefly introduced.

Keywords

💡Arithmetic Instructions

Arithmetic instructions refer to the set of commands that perform mathematical operations on data. In the context of the video, these instructions are fundamental for data manipulation within a computer's CPU. They include operations like addition, subtraction, multiplication, and division. The video emphasizes how these operations are not just abstract concepts in programming languages but are also executed by the hardware, showcasing the interplay between software and hardware.

💡Data Manipulation

Data manipulation involves the processing and modification of data within a computer system. The video script discusses how arithmetic instructions play a crucial role in data manipulation, as they allow for the fundamental mathematical operations that are necessary for various computations. This is illustrated by the example of performing multiplication through repeated addition.

💡CPU

CPU, or Central Processing Unit, is the primary component of a computer that performs most of the processing inside the computer. The video script explains how the CPU, through its Arithmetic Logic Unit (ALU), executes arithmetic instructions. It highlights the efficiency of having hardware support for these operations, as opposed to software emulation, which can be less efficient.

💡ALU

ALU stands for Arithmetic Logic Unit, a part of the CPU that performs arithmetic and logical operations on data. The video explains that the ALU is responsible for executing arithmetic instructions like addition, subtraction, and more complex operations like multiplication and division, which can be achieved through repeated use of these basic operations.

💡Increment and Decrement

Increment and decrement are operations that increase or decrease a value by one, respectively. In the video, these operations are discussed in the context of registers, which are components used for storing data temporarily. Incrementing or decrementing a register is a common operation in programming, often used for counting or adjusting values by one unit.

💡Micro Operations

Micro operations are the low-level, detailed steps that a CPU takes to execute a higher-level instruction. The video script explains that an instruction like addition involves several micro operations, such as fetching the instruction from memory, decoding it, and then performing the actual addition. This concept helps viewers understand the complexity behind simple operations.

💡3-Address Instruction

A 3-address instruction is a type of instruction format that includes three addresses: two for source operands and one for the destination. The video script uses this concept to explain how an instruction like 'C = A + B' is executed, where A and B are source operands, and C is the destination. This format allows for clear understanding of where data is coming from and where it is going.

💡Carry

Carry refers to the value that is generated when the sum of two binary digits exceeds the maximum value that can be represented by a single binary digit. In the video, carry is discussed in the context of addition, where it is necessary to handle overflow in binary arithmetic. The script mentions how carry is stored and used in subsequent operations, which is crucial for accurate computation.

💡Borrow

Borrow is the concept used in subtraction when the minuend is smaller than the subtrahend, requiring 'borrowing' from a higher place value. The video script explains this in the context of binary arithmetic, where a borrow might be needed when performing subtraction. It is an essential part of arithmetic operations to ensure the correctness of the result.

💡NEGATE

NEGATE is an instruction used to change the sign of a number, effectively converting it to its additive inverse. In the video, the script mentions how the NEGATE operation is used to represent a number in its negative form, such as changing a positive number to a negative one. This is typically done using the 2's complement method in computer systems, which is a fundamental concept in arithmetic operations.

Highlights

Arithmetic instructions are fundamental for data manipulation in programming.

Basic arithmetic operations include addition, subtraction, multiplication, and division.

Multiplication can be achieved through repeated addition in a loop.

Division can be performed by looping subtraction.

Modern commercial systems include hardware for arithmetic operations for efficiency.

The Arithmetic Logic Unit (ALU) is responsible for performing arithmetic operations.

Increment and decrement operations are used to adjust values by one in registers.

Registers are collections of flip flops that can be used as counters.

Instructions and micro operations are different; instructions are higher-level, while micro operations are the internal steps.

The process of executing an arithmetic operation involves instruction fetch, decode, and execution.

Addressing modes like immediate, direct, and indirect affect how operands are accessed.

Three-address instructions include source, destination, and operation within a single instruction.

Carry and borrow are important concepts in arithmetic operations, used for multi-digit calculations.

The NEGATE instruction is used to represent a number in its negative form.

The 2s complement method is used to convert a positive number to its negative equivalent.

Variations in arithmetic instructions depend on the data type and addressing mode used.

Understanding the backend operations of arithmetic instructions is crucial for optimizing performance.

Transcripts

Hello friends, welcome to Gate Smashers

In today's video we are going to discuss about arithmetic instructions

Like arithmetic instructions come in data manipulation

In which arithmetic is logical and we have shift instructions

So in arithmetic we have, like we use in programming language

Arithmetic operations, like in C language we do addition of two numbers

multiplication of two numbers, subtraction

of two numbers or division of two numbers

The arithmetic operations we use in general programming language

How these operations are performed on the backend

Backend means how the computer's hardware, the CPU

How it performs by using these instructions

So first of all we have addition and subtraction in arithmetic

So if we talk about any basic computer, from basic to basic

If we talk about small to small computer

Then at least we have subtraction and addition in it

And with the help of these we can perform multiplication or division

Like if we talk about doing 2*3

Now to do 2*3 I have another method too

If I add 2 three times then the answer will be same

So here we can execute multiplication with the help of addition

Means we have to execute the program in

such a way that we run addition in the loop

If we talk about subtraction

With the help of subtraction we can do

division if we run subtraction in the loop

But if your hardware, because today all the commercial systems we are using

There at least we have subtraction, addition, multiplication and division

If not then we will get less efficiency there

because there is no proper hardware for it

So we have to do these with the help of program

But if we have hardware available then we will get optimized answer

Means the answer will come as soon as possible So these are four things

Addition, subtraction, multiplication and division

For this already hardware is available

The ALU basically performs So with the help of these four

The rest of the mathematical operations like exponential, logarithm

Whatever type of operations we can perform with the help of these four

So it completes all the mathematical expressions in a way

Next if we talk about increment and decrement

What is the meaning of increment?

Which we denote as INC Increment means if we talk about simply.

That I have to increment the value by one Or decrement by one

So basically increment and decrement is that we use it in registers

Like registers are a collection of flip flops

And how can we make the collection of flip flops as a counter

So we can simply increment it through one clock pulse in the counter

We can also decrement it But how will it happen?

How will ALU know?

How we have to distribute that value to the register

We do that through increment and decrement through instruction

Here students get confused many times

What is the difference between instruction and micro operation

Means we are using the word instruction generally Like addition, subtraction

What is micro operation?

Micro instruction

Instruction is a big term

To perform this ALU or processor has to follow more steps internally

For example if we talk about I have to do this C=A+B

Means I have to put addition of A+B in C

Now here I have written in normal programming language C=A+B

But how will the computer do this?

So when the code will compile and become executable

So it will be stored in the instruction

Where I have up code and apart from up code there will be operand

Now if we talk about multiple ways

We have 3 addresses, 2 addresses, 1 address, 0 addresses

Let's talk about if we have 3 address instruction What does 3 address mean?

Means we have 3 addresses means we have

source, destination And we have 2 sources here

Their address is also here

Means you will get source and destination address in one instruction

And what you have to do?

If you have to add in between, you will get the operation you have to perform

So let's say C=A+B So what will happen is C is destination

A and B are sources here So whatever addressing mode we are using

If we are using immediate Then we can directly take the value from here and add

If we are using direct or indirect Then their address will be given here

Which we will discuss in detail in addressing mode

But what it mean to say here is

That simple addition is not that it will work by writing

Multiple operations are performed at the backend

First of all what happens is instruction fetch.

Means the instruction you have stored in memory

You have to pick it up from that memory and bring it to the instruction register

What will the instruction register do next?

It will decode the instruction Now when we decode the instruction

Then we will know where the operand is Means where is the value of the operand

And after that we will know after decoding that up code

Means what to do When we get only one value after decoding

Will get only B value and what to do in

between When all this work will be performed

Then the entire command will be stored there

Means the entire instruction will be executed then

So there are micro operations at the backend

There are small operations which are performed at the backend

Which we will see in detail in the instruction cycle

But here I am giving a basic overview

How addition, subtraction, multiplication,

division work And if we have hardware available

Then our result will come soon and will be optimized

Otherwise we can run it in the multiplication loop.

Apart from this if we talk That the instruction we have

This instruction basically depends on how your

hardware is Or what data you are working on

Means if you are adding two integers or two floating point numbers.

Then on the basis of that it depends

How we have to take the instruction

How to use it Because this instruction

internally As I told you in the last video also

In which we discussed the video of data transfer

So in data transfer also multiple variations are possible in one instruction

And these variations are based on hardware

Based on the data you are working on

or based on what addressing mode you are using

Means there are multiple variations in these instructions Which we use

Then increment, decrement is done Add with carry

Add with carry means that sometimes when we add two numbers

Then what comes there, carry comes Now what we are doing with carry also

Obviously we have to store it Because next time we may have to use that carry

Let's say if we talk about 1 1 0 1

So let's say here 1 1 means 0 and what is this 1

And again 1+1 means 0 and 1 is made here carry.

So what we will do with this carry

Next time we will execute the instruction So I will have to use it there

If we talk like this Subtraction with borrow

means if we subtract here Let's say 1 0 0 1

So what I have to do here I have to carry from here When I carried this

Means carry in the sense that I have to borrow here

So when we borrow here So what I have to keep that bit too

I have to store it so that we can use it in the next instruction

So carry and borrow, we use both of them

So in some instructions where carry and borrow is used

So there we execute them with the help of these instructions Then we have NEGATE

NEGATE we generally use to represent the

number in minus Let's say if we have a number 5

And I have to change it to -5.

So we generally use NEGATE And what we do in real life environment

How do we convert 5 to -5

By using the 2s complement So we do it with the help of 2s complement

But how does the processor do it on the

backend What do we give instructions here

Here is NEGATE So this is the basic stuff of arithmetic instructions

But remember that there are multiple variations in the instructions

They depend on which data you are working on

Are you working on floating number or on integer

Or which addressing mode you are working on

So based on that some changes keep happening here Thank you.