All things in all posts will help you visualize about the way that computers work generally. Note that it is not the real structure of modern computers, but the way that modern computers work is nearly the same as in my posts. I am sure that if you understand about the way that computers work in my posts, you will easy to learn about all fields of computer afterward. Thank you !!!
All gates that we used have two input signals (bits) in previous posts. So, how can we use gates that have three input signals or more? The answer is that we will connect more than one gate together to have more input signals. Look at the picture below to understand about it:
On the left of the picture, you can see two AND gates are connected together. The output signal of the first AND gate (bit) is the input signal of the second AND gate. So, you can think of those two AND gates as only one AND gate that has three input signals on the right of the picture. You may wonder about the truth of this conversion. Do not worry because it is completely true. Look at the truth table for two diagrams in the picture below to understand:
The truth table above is the same for two diagrams in the picture. One thing that you should remember is that you can use AND gate for any number of input signals: four, five, six,...not only three. That is a really interesting thing. And you can also represent all of them in a diagram that contains all two-inputs AND gates (standard AND gates).
If you notice the details in the truth table above. You can see that we have 8 combinations for three input signals. As I mentioned in a previous post, if we have n input signals, we can have 2n combinations. So, here we will have 23 = 8 combinations easily. Similarly, when we have 4 input signals, we have 16 combinations,...But one thing again that you should remember is that only the combination containing all 1 (on) signals (bits) will return output is 1 (on) signal (bit).
From the combination AND gate above, we will construct an important device in computers. First, you look at the picture below to understand another diagram that help you to understand that device easily:
In the picture above, you can see two input signals, two NOT gates and four AND gates. First, we have two input signals connected directly to AND gates with each input signal for two AND gates so each AND gate only has one input signal now. Next, two input signals above go through two corresponding NOT gates then each of them also connect to four AND gates. Now, we have a complete diagram.
We will have four combinations for the two input signals above. With the “0/0” combination for input signals, you can see that only the first AND gate will have an output signal “on” (1). Others are in “off” (0). So that first AND gate will be the gate for input signal pair “0/0”. With “0/1” combination, you can also see the similar thing but this time it is for the second AND gate. So we will also call the second gate the gate for input signal pair “0/1”. Similarly, the third gate is the gate for input signal pair “1/0” and the fourth gate is the gate for input signal pair “1/1”.
We will also have the truth table below to you can understand more about this gate combination:
The name of that combination is decoder. You can understand that name easily. We have four combinations of input signals, with each input signal pair, you can have only one AND gate that is “on” for output signal and that AND gate is only “on” when that input signal pair appears.
The decoder above is small and is called a 2x4 decoder because with two input signals, you can have four combinations. Similarly, we can have 3x8 decoder, 4x16 decoder,...Below is an another example about 3x8 decoder that use three inputs AND gate in the first part of this post:
The way that this 3x8 decoder works is similar to the 2x4 decoder, so you can do it yourself and I will not repeat again. But we will build a larger structure so we can not use this complex diagram in that structure. We will use a symbol to substitute for it because you understood the way that it works. Look at the picture below:
All symbols in the picture are easy to understand so you can do it. You can see that we built parts from smaller things then symbolize them and continue the same things for the bigger parts of computers. So you can understand from small structures to bigger structures and you do not feel so difficult. Such as from NAND gates, you can build NOT gates and AND gates then we symbolize those gates. We built decoders from NOT gates and AND gates then we symbolize them again. We always perform that process in all my posts. Thanks for reading and see you again.
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