4.2. Building Blocks of Digital Computers

When we talk about digital computers necessarily another question will come to our mind that is there some other computers are there. In that case you can categorize the computer in two broad categories, one is a digital computer and second one is an analog computer.

Digital computers are based on binary logic, using two states (0 and 1) to represent data. In contrast, analog computers use continuous signals for measurements. Understanding the distinction between these types of computers is crucial for grasping the fundamentals of digital computer architecture.

Think of digital computers like light switches that can either be turned on (1) or off (0), while analog computers are more like a dimmer switch that can be adjusted anywhere between fully off and fully on, allowing for a smooth range of settings.

So, in case of analog computer we work with continuous signal. For example, say you are having the voltage speed in x-axis we are having time and y-axis say we are having voltage. These electrical signals flow continuously then we say this is your analog signal. In case of digital computer we are going to sample these signals at particular instances of time.

An analog signal can take any value within a range, while a digital signal can only be one of two states. Digital computers sample analog signals at specific intervals, allowing them to convert continuous data into discrete data, which can be manipulated more easily by digital circuits.

Imagine recording music on a vinyl record as an analogy for analog signals where the grooves represent the continuous sound. In contrast, saving music as a digital file, where the sound is captured only at certain intervals, represents discrete signals.

Finally, what will happen? We are coming down to some number system which is your binary number system. So, digital computer works on binary number system.

In a binary system, data is represented using only two digits: 0 and 1. This simple system underlies all digital computing processes and allows for the complex calculations and data handling required in digital electronics. Each binary digit (bit) represents a state of the signal.

Consider a lightbulb that can either be off (0) or on (1). Every piece of digital data is built upon these 'on' and 'off' states, similar to how a series of light switches can create various light patterns.

In case of digital circuits, any digital logic function is represented by Boolean expression. Digital logic circuits can be categorized into two different categories one is your combinational circuit and second one is your sequential circuit.

Combinational circuits are those where the output at any time depends only on the current inputs. In contrast, sequential circuits have outputs that depend not only on current inputs but also on past outputs, thus using memory for their functioning.

A combinational circuit can be thought of as a recipe where the output (meal) depends solely on the current ingredients used (inputs). A sequential circuit, on the other hand, is like making a layered cake, where the final outcome (the complete cake) depends on the previous layers (previous outputs) as well as the current ingredients.

So, in that particular case we are going to have the same gates like AND, OR, NOT, and we will also look at how they can be combined to form complex functions.

Logic gates perform basic logical functions that are foundational to digital circuits. For instance, an AND gate outputs high only when all its inputs are high, while an OR gate outputs high when at least one input is high. This functionality forms the basis of building more complex operations and circuits.

Think of AND and OR gates like decision-making processes. An AND gate is like a requirement where everyone must agree before acting, whereas an OR gate allows for any one person to make a decision for the group, fostering quicker responses.

The first circuit I am going to talk about here is your half adder this is basically adding of two numbers.

A half adder takes two binary inputs and produces two outputs: the sum and the carry. For example, when adding binary numbers 1 and 1, it produces a sum of 0 and a carry of 1. This concept scales up in more complex circuits like full adders, which account for carry-in values from previous additions.

Consider counting bricks. If you have one brick and add another brick, you immediately recognize that you have 2 bricks (output = sum). But if you are stacking them, you might need to carry one over if you can't stack taller, which illustrates the carry output.

Now, we are having another circuit called decoder. Here we are having n input lines and m output lines.

Decoders convert binary information from 'n' input lines to a maximum of '2^n' output lines, ensuring that only one output is activated based on the input combination. Encoders work in reverse, taking '2^n' input lines and converting them into 'n' output lines, effectively reducing multiple signals into fewer signals.

Think of a decoder as a restaurant menu that allows you to choose from multiple options, where each unique combination of inputs corresponds to a different dish (output). An encoder can be related to giving a voting results summary where each dish's popularity is summarized into just a few results.

So, it is basically going to multiplex or masking some of my input signals.

Multiplexers select one of many input signals and output that single signal based on select lines. They help manage multiple signals by reducing them to one output line to prevent overload in circuits, making layouts simpler and more efficient.

Imagine a switchboard that connects various phone lines to a single operator. Only one line can be connected at a time (multiplexed), allowing the operator to handle multiple conversations without confusion or interference.

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