25.5.2. Signal Count Analysis

So, this is just again very quickly very quickly let us look at now we are going to take a more elaborate depth with more clear examples that, optimization is done on the signals by encoding. So, last unit we have already discussed that encoding is very important. So, if you encode basically what is going to happen? If there are n control signals in the CPU, the length of each control word of the memory will be n very simple there is a horizontal micro program everything is parallel. This is actually a horizontal micro program and it is going to be very fast, but the memory is unoptimized.

In this section, we discuss how the optimization of control signals is achieved through encoding. Encoding helps in reducing the number of control signals, making the CPU more efficient. For example, in a horizontal microprogram, if there are 'n' control signals, the control word length is 'n', which allows for parallel execution, enhancing speed. However, this approach leads to memory inefficiencies, as such a structure can consume significant memory resources without optimizing the signal usage.

Imagine trying to send a long message using a wide array of individual letters (like using many control signals) which makes it quick to send, but wastes a lot of paper. Instead, coding it into a shorter version allows one paper to convey the same message more efficiently, which is similar to how encoding simplifies signal transmission in CPUs.

To do this we have seen that in the last unit, that we have to optimize by encoding the signals, which is actually called the vertical micro instruction. So, if you just go for a very flat compression that is from 2𝑛, we just compress it to 𝑛 or from 𝑛 to 𝑙𝑜𝑔 𝑛 and using 𝑛 to 2𝑛 decoder, then actually full compression is there and this is actually called a full vertical micro program. But in this case only one bit signal can be made a 1. So, if simultaneously 3 or 4 points to be a 1 you require 4 cycles for that.

Vertical micro instructions are a method of compressing control signals to improve memory efficiency. By compressing from '2n' to 'n' or from 'n' to 'log n', we achieve significant reductions in the number of signals needed, referred to as full vertical microprogramming. However, a downside arises with this approach, as only one signal can be active at any moment, which may require multiple cycles for simultaneous operations, potentially slowing down processing when multiple signals need to be high at once.

Think of trying to manage a busy office with a single phone line (indicating a single active control signal). You can only talk to one person at a time. If you need to talk to multiple people simultaneously, you'd need to call one after another, wasting time—similar to how vertical instructions handle signals one at a time, slowing down overall operations.

So what we basically do is that, we go for basically something called a hybrid approach in hybrid we make clustering and for each clustering we will try to put signals in one cluster, which need not be simultaneously 1. So, that is one idea of actually called a hybrid micro program.

The hybrid approach combines the advantages of horizontal and vertical micro programs by utilizing clusters of signals that are not required to be active simultaneously. This leads to better organization of control signals, allowing for a more efficient use of memory while maintaining speed in processing because we avoid the overhead of requiring multiple cycles to switch active signals.

It's like organizing a team project where different groups (clusters) work on their parts independently and only meet when necessary. Instead of all team members just waiting around (like simultaneous signals), they focus on their tasks and come together when they need to share information, thus speeding up the project completion.

So, let us count how many input and output ports are there. So, 1 2 there are 7; 4 user registers, 3 system registers 7 into 2 14 then 15 16 17 18 19 20 21 22, 23 I miss something 1, 2, 3, 4, 5 6, 7 8, 9, 10 sorry 10; 10 over here, and 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 20 actually there are 24 signals will be there.

The section recounts the number of input and output signals necessary for the CPU's effective operation. It illustrates how these signals can accumulate quickly due to several registers and their input/output requirements, highlighting a total of 24 signals needed according to the architecture outlined.

Imagine a bus station where each bus (register) has multiple stops (signals). Each route requires a different set of instructions to manage where to stop and let passengers on or off (input/output signals). If you have many buses needing to operate, you quickly realize how many routes and stops you must handle, just as the CPU requires numerous signals to manage its operation.

So, therefore, basically 46 will be the length of the micro program and it has been found theoretically that only 10 to 15 % of the memory positions are 1. So, if we have such a big array whose size is 46 and it will be long depending on how many micro instructions are there, and only 15 % is actually filled with 1 is a huge waste of memory.

As illustrated, the micro program can require up to 46 bits, and it's identified that only a small fraction of these (10-15%) are actively utilized at a given time. This results in significant memory waste, as a considerable portion of the memory remains underutilized due to the broad width of the micro instructions involved.

Think of renting a conference room (micro program) that's large enough to hold 200 attendees (46 bits), but only 20 people show up (10-15%). You still pay for the entire room, even though most of it goes unused. This demonstrates how inefficiently resources can be managed when excessive capacity is provided without regard for actual needs.

--