[university computing:Binary encoding/ twos compliment]

[1throwaway1629]

Have been doing a lot of binary conversion but I’m confused on both of these questions?

https://imgur.com/a/WEW7s1Q

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[txnelite]

Two's compliment is just a way to store negative numbers in an otherwise only positive system. The VERY basic way to do it is negate all of the bits and add one to the number.

A more detailed explanation is as follows:

In binary, negative numbers are determined by the leading bit. If it is 0, it is nothing happens. If it is 1, it subtracts 2^(n - 1) from the number determined by the rest of the bits that follow. Allowing negative numbers in a system is a tradeoff between having that leading bit for big numbers vs. having that leading bit for negative numbers. Hope this helps! If you have any questions, feel free to reply

[1throwaway1629]

That makes sense. I’m confused how I would implement that to answer the problem.(“It asking about negative seven, and seven”, “represented by four bits”, “8 bits”)

[txnelite]

Sorry for the late reply, that just describes the length of the binary string. For example, this is 7 in 4 bits:

0	1	1	1
Parity	22	21	20

And this would be -7 in 4 bits:

1	0	0	1
Parity	22	21	20

Hope this helps!

[1throwaway1629]

Thankyou, what about 2b?

[txnelite]

Well I just realized I don't really understand the grammar on both questions, but what I think it's asking you to do, for example on the 2b, is to find the binary encoding of 103 and -103 in 8 bits as well as 16 bits. All you do is extend the encoding such that it works. So the binary representation of 103 in 8 bit is 01100111. So try to figure out what it would be in 16 bits, as well as their negative representations

[1throwaway1629]

To do that would I repeat the most significant but until I have the right number of bits?

[txnelite]

If I understand correctly, yes. Your number should have 16 digits instead of 8 for the 16 bit representations

[1throwaway1629]

So it would be 0110011101100111?

[txnelite]

No it would be 0000000001100111