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If i subtract 1110 from 1001 using 2's complement method, then the result is (-)1011 . But it should have been (-)101 . Why does this happen? Is 2's complement method is inadequate? Or there's something i'm missing?
Solved.
I didn't knew negative numbers were represented a bit different on 2's complement. It seems that negative numbers in 2's complement are represented such that it yields 0 when added to the additive inverse.
More on : academic.evergreen.edu/projects/biophysics/technotes/program/2s_comp.htm
Related
I'm having some difficulty understanding how I would go about doing this. I've been given some binary numbers to convert to decimal with the question saying:
Convert the 2's complement numbers below to decimal
#1 : 1001
#2 : 0010
For #1 I know you would just take the 2's complement to find the magnitude because the 1 indicates it's negative. So it would really be 0111 or -7. What I'm having trouble with is if I should do the same process with #2. It's not negative so I don't know if the problem wants me to instead take the 2's comp or if the decimal would just be 2?
I've been given the directions
Add the following binary 2's compliment representation values
in 16 bits, then write "overflow".
0001 0101 0111 1101
+ 0111 1111 1011 1111
I've tried to understand 2's complement, and I do to an extent. But, I'm still not clear on several things. Is 2's complement only used for negative values? I think how I would solve this problem would be to start by taking each number, inverting it, adding 1, then adding them together. Is this the proper way to do it?
Thank you
Two's compliment is a representation for handling positive and negative values in a way that allows you to follow the mechanics for doing addition as if they were positive values, but end up with the correct result even if either or both values represent negative values.
Taking the two's compliment is used to change the representation to be that of the negative of the value you started with. Since you are not asked to negate anything, you should not be doing this.
I want to design a hardware which will give 2's complement of input 4-bit binary number. But i stuck at very first input: 0000.Because the method i generally use to find 2's complement is to first find 1's complement of binary number and then adding 1 into it.But if I do same with 0000, then it will give me 5-bit number 10000. that is the problem.
You have to cut off the upper bits if you're working with an n-bit value. The two's complement of the four-bit 0000 is the last four bits of 10000, or 0000. Otherwise the ones' complement of 100 would be:
1111111111...ad infinitum...1111111011
rather than the correct 011.
That (the cutting off of extraneous bits) makes sense since the negation of zero is zero (though that could be arguable for ones' complement or sign-magnitude, where -0 is a distinct possibility).
If you design hardware, see hardware circuits for produce 4-bit complement number.
I need help in determining if my logic here is right or wrong.
Example Question
"Assuming I have an 8-bit signed decimal value of 200 in two's compliment form..."
My Thought Process
Now because it is 8-bits and is signed, the most significant bit must be reserved for the sign.
Thus, the maximum positive value it can have is:
2^(8-1) - 1 = 127
At first I was confused because I thought, why is the question stating that 200 is able to be 8-bits and signed? Then I thought, that's where the two's compliment statement comes into question.
Because it is two's compliment in reality, this is the case:
8-bit Signed, 2's Compliment, Decimal = 200
Convert to Binary --> 1100 1000
Because it is signed, the actual two's compliment number is ACTUALLY -56 (I would use negating methods to invert the 1's and 0's then + 1, but for the interest of time, I just found a converter online).
So my conclusion is:
8-bit Signed, 2's Compliment, Decimal value of 200 is actually -56.
Ultimate Question
Is my thought process correct with this? If so, I think the most confusing part about this is telling my brain that one number is equal to a completely different number.
Yes, I think your analysis is correct.
To expand a bit more, I think the wording of the question is awkward and would have been better stated as "What is the value of 1100 1000 in base 10, where the number is a two's complemented number?"
The trick here is to think not that 200 == -56, but that the single point of truth is the bits 11001000. These bits of numbers have no meaning by themselves. We have the computer interpret them differently based on the program. So two's complement (with 8 bit numbers) treats that as -56, an unsigned interpretation would treat that as 200, and in ASCII this would be some special character depending on the encoding.
(Not sure if I am allow to ask a question like this but will delete if asked)
Convert -25 into binary representation using 8 bits and 2's complement format to represent a negative number. So far I got 11001.
I tried to google methods but I am not sure how to do it using the 8 bits way.
This question is not using code, just conversions but from what I did was
convert it to binary which was 11001 then I added 3 zero's to make it 8bits (assuming that is correct) 00011001 then I did 1's complement 11100110 and 2's complement by adding 1 which equals 11100111.
I am not sure if that is correct.
Two's complement is probably one of the more straightforward operations on binary numbers. In short, you'll want to take the following actions to convert a decimal number into two's complement form:
Write down the binary representation of the positive version of your number. In this case, 25 should be represented as: 00011001
Next, flip all the digits: 11100110
Add one: 11100111
Sit back, grab a drink, and bask in the glory of the newly-created two's complement representation of a decimal number.
Source
1.assume the negative sign and get the binary of the positive integer.adopt 8bit notation
25--00011001
2.get the two's complement.
11100111
+ 1
=11111000
3.relax and enjoy the two's complement