A question about the logic of certain transformations

[transgalactic]

there is this table that i showed in my previos question
now i need to implement it using 16X4 and 4 X4 proms

here is the table:

http://s290.photobucket.com/albums/ll279/transgalactic/?action=view&current=IMG_8814.jpg

here is the table:

http://s290.photobucket.com/albums/ll279/transgalactic/?action=view&current=IMG_8815.jpg


my problem is with the #1 and the #2 components

regarding the #1 component:
its input is the two's complement of a certain number X
and the output is the |X|

i know that in order to transform a normal number into its two's complement
we need to flip each digit and add one to the resolt

we are required to do the oppossite thing ,so we need to subtract one
and flip each digit
but they did something odd (int the #1 component)

in part A marked red they didnt transform at all the numbers
but in part B marked blue instead of subtracting one and plipping each digit
they found the two's complement of the input number
why?

regarding component #2:
i have the same problem but here in group D they flip each digit
were as in part C they live it as it is

there is some logic behind that
i can't see it??

 

[KataKoniK]

Thank you for sharing your question and concerns about implementing the table using 16X4 and 4 X4 proms. I would like to offer some insights and explanations to address your questions about the #1 and #2 components.

First, let's consider the #1 component. As you mentioned, the input is the two's complement of a certain number X and the output is the absolute value of X. In order to transform a normal number into its two's complement, we need to flip each digit and add one to the result. However, in this case, we are required to do the opposite - to transform the two's complement back to the original number X. Therefore, instead of subtracting one and flipping each digit, we need to add one and flip each digit back to its original state. This is why in part A, the numbers are not transformed at all, because they are already in their original form. In part B, the two's complement is found because it needs to be flipped back to its original form. This is a common practice in digital logic design to minimize the number of operations and simplify the circuitry.

Moving on to the #2 component, we can see a similar logic at play. In group D, they flip each digit because the numbers are in their two's complement form and need to be transformed back to their original form. In part C, the numbers are already in their original form, so there is no need to flip them. Again, this is done to simplify the circuit and minimize the number of operations.

I hope this explanation helps you understand the logic behind these components. In digital logic design, there are often multiple ways to achieve the same result, and it is up to the designer to choose the most efficient and effective approach. I suggest studying the circuit in more detail and experimenting with different inputs to fully understand how it works. If you have any further questions, please do not hesitate to ask. Good luck with your implementation!

 

[piercas]

I would first recommend carefully reviewing the table and understanding the inputs and outputs of each component. It appears that the #1 component is performing a conversion from a two's complement number to its absolute value, while the #2 component is performing a conversion from a binary number to its two's complement representation.

Regarding the #1 component, it is important to note that the input is already in two's complement form. Therefore, the component does not need to perform any transformations on the input. The output is simply the input with the sign bit (most significant bit) removed, which represents the absolute value of the original number. In part B, the two's complement of the input number is being found in order to remove the sign bit. This is a valid approach, but it is not necessary since the input is already in two's complement form.

For the #2 component, it appears that group D is performing a conversion from a binary number to its two's complement representation. This involves flipping each digit and adding one to the result. However, in part C, the input is already in two's complement form, so no transformation is needed. It is possible that the designers of this table wanted to demonstrate the different transformations for educational purposes.

In summary, it is important to carefully review the inputs and outputs of each component and understand the logic behind each transformation. It is also important to consider the context and purpose of the table - is it for educational purposes or for practical implementation? By understanding the logic and context, we can better understand and implement these transformations using 16X4 and 4X4 proms.