23.2.1. Memory Size and Steps

So, whenever we want to optimize based on encoding or compressing of the signals in each of these cells or each of the words in the program control memory, we call it as a vertical micro-program. In horizontal it is very flat and no optimization is there.

This chunk introduces two types of micro-program structures: vertical and horizontal. A vertical micro-program optimizes memory by compressing signals, while a horizontal micro-program is simpler and does not optimize memory usage. The vertical approach is akin to summarizing information to save space, while the horizontal is like listing everything out without any reduction.

Think of a vertical micro-program as a condensed book summary that provides all the important points in a few pages. In contrast, a horizontal micro-program resembles the full book with every detail included, which takes more paper.

So, basically first the most formal or the preliminary way of doing it is basically encode the signals in the control memory.

Here, the focus is on the method of encoding signals in control memory. Encoding transforms information into a format that reduces the amount of data needed to represent the control signals, leading to better use of memory space. This is done before using a decoder to retrieve those signals when needed.

Imagine encoding is like compressing a video file. You take the original video, reduce its size without losing crucial details, and store it. When you want to watch it, you decode it back to its original format.

So, I just put a 3:8 decoder then, what will be the memory size? The memory size will be 3 bits.

This chunk explains how decoders are used to reduce the memory size needed for control signals. A 3:8 decoder can take 3 bits of input to produce 8 outputs, allowing only one of these outputs to be activated at a time. This drastically reduces the number of bits required to control multiple signals.

Think of a decoder like a light switch control panel. If you have 3 switches (inputs) controlling 8 lights (outputs), you can only turn on one light at a time, making it easier to manage instead of having a switch for each light.

So now, you have to observe that this is one of the drastic way of compressing. So, instead of 2n the size will just become n or if it is n you will go for log n upper ceiling.

This explains the efficiency of vertical micro-programs, illustrating that by encoding signals, the size can decrease dramatically, often illustrated as a shift from needing 2^n to just 'n' or 'log n'. However, this has limitations - only one output signal can be active at any time, which can slow down operations.

Consider a city with one main road (representing compressed control signals) where only one car (signal) can drive through at a time. Even though this single road helps reduce traffic (memory usage), it can also lead to backups if multiple cars need to go through simultaneously.

But now, simultaneously you cannot also make MAR = 1.

This section discusses the operational limitations of vertical micro-programs, particularly regarding the Program Counter and Memory Address Register. Because only one control signal can be active at once, processes that normally work together (e.g., the PC and MAR) now must be handled in sequence, causing delays.

Imagine trying to fill two bowls with water (PC and MAR) using a single tap (the vertical micro-program). You can fill one bowl at a time, resulting in slower service rather than filling both bowls simultaneously if you had two taps.

But, the advantage is that the memory size actually gets compressed in the value of in the terms of log from 2n, it will go to the order of n.

This chunk highlights the main trade-off of vertical versus horizontal micro-programs. While the vertical approach reduces memory usage significantly, it requires additional time and steps to execute processes, leading to a slower overall performance compared to a horizontal micro-program, where signals can act in parallel.

Think of horizontal micro-programs like a well-staffed restaurant where multiple tables (signals) can be served at the same time, leading to faster dining experiences. In contrast, a vertical micro-program is like a solo chef who can prepare one dish at a time – it's efficient in resource use but slower overall.

So, what is the cluster idea I will take a figure and then I will come back to the theory.

This chunk introduces the concept of clusters, which are groups of signals organized to allow for simultaneous activation of signals within the same cluster while still maintaining the memory efficiency of the vertical approach. The cluster technique combines elements of both vertical and horizontal micro-programming, increasing efficiency while allowing more flexibility in processing.

Think of clusters as study groups in a classroom. In one group (cluster), students can discuss and share ideas simultaneously without disrupting each other. This setup allows for collaborative learning while still ensuring each student retains their individual insights and work.

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