5.2.1. Basic Processing Element

Another one we are having Demultiplexer which is the reverse of your multiplexer. So, here we are having 1 input line and we are going to transfer it to any one of those particular output line. So, if we are again I can say that input line is 1 output line n then what is how many select line we have? Again this is your ⌈𝑙𝑜𝑔 𝑛⌉. So, we are having 1 input lines now we are having 2 select lines, depending on those particular select line we are going to transfer this input line to any one of those particular output lines.

A demultiplexer (or demux) is the opposite of a multiplexer. While a multiplexer takes multiple inputs and sends them to a single output based on control signals, a demultiplexer takes a single input and directs it to one of many outputs. Here, if we have 1 input line and we want to distribute this to 'n' output lines, the number of necessary select lines is determined by the formula ⌈log n⌉. For instance, if you have four outputs (Y0 to Y3), you will need two select lines to determine which output will receive the input signal.

Imagine a postal service where one letter (the input) needs to be delivered to one of several houses (the outputs). The houses represent the different outputs of the demultiplexer, and the address (determined by select lines) specifies which house receives the letter. Just like the postal service selects the appropriate house based on the address, a demultiplexer selects a specific output based on its inputs and select lines.

Another unit we are having called arithmetic and logic unit, ALU. This is the basic processing element inside of computer which can perform some arithmetic operation and logic operation.

The Arithmetic and Logic Unit (ALU) is a core component of a computer's processor, responsible for carrying out arithmetic operations (like addition, subtraction, multiplication, and division) and logical operations (like AND, OR, NOT, and XOR). The ALU processes binary numbers and delivers results based on the operation selected for two input values, generally represented as 'A' and 'B'. This unit is critical for the functioning of any computing task, as it handles the calculations and logical determinations necessary for data processing.

Think of the ALU as a chef who can perform different recipes (operations) based on the ingredients (inputs) you give them. For example, if you want to make a cake, the chef follows a recipe (like performing addition) to combine flour and sugar. Similarly, if you need to prepare a salad, the chef will follow a different recipe (like performing logical AND operation) to combine vegetables. The ALU, like the chef, can switch between tasks depending on what is required at the moment.

So, I am having 4 processing element which can perform operation addition, subtraction, multiplication and division. So, these are the say 4 arithmetic operation we have. Along with that we may have some logical operation also logic operation also, I can say that I may have that AND operation, OR operation or maybe say XOR operation or maybe I can say another one say NOT operation.

The ALU can perform four main arithmetic operations: addition, subtraction, multiplication, and division. These operations allow it to handle numerical data effectively. In addition to arithmetic operations, the ALU also performs logical operations, including AND, OR, XOR, and NOT. Logical operations are crucial for making decisions based on binary inputs, where the results influence how the ALU processes data in programs and algorithms.

Picture a Swiss Army knife, which has multiple tools for different tasks. The arithmetic operations (addition, subtraction, etc.) are like the knives and scissors that cut through materials, while the logical operations (AND, OR, etc.) are like the screwdrivers and can-openers that are used for specific jobs. Just as a Swiss Army knife can handle a wide variety of situations and tasks, the ALU can perform numerous calculations and logical tests to fit the needs of different software applications.

Now, at any point of time we are going to give 2 inputs over here A and B, and we are going to perform 1 operation and depending on the operation we are going to get our result. Now, how we are going to select this particular operation? ... So, when this third bit I am going to put as 1, then I can say that I am going to use those particular logic operation.

For the ALU to operate, it needs to know what type of calculation or logical operation to perform on the given inputs 'A' and 'B'. This is accomplished using control signals defined as operation codes (opcode). Depending on the opcode generated, one of the various functional units in the ALU (for instance, the adder for addition or a gate for AND operation) is selected to process the inputs. Thus, with appropriate control signals, various operations can be performed sequentially or concurrently.

Think of a remote control for a TV which allows you to select different channels or adjust volume. Each button (like an opcode) corresponds to a different function (operation) like volume up (addition) or mute (logical operation). Just as you would press a button to change the function of the TV, opcodes guide the ALU on which operation to execute based on the input signals.

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