(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
Related
For example, we're given the number -1.5(10).
Converting it to signed binary we get 11.1000(2).
Its two's complement is 00.1000(2), which is 0.5(10) when converted to decimal.
Which is self-explanatory, because it's a different binary number.
What else is there to explain?
You are mixing apples (signed-binary) and oranges (two's complement).
You took a negative value in one representation (signed-binary), negated it using the technique for a different representation (2's complement), and (unsurprisingly) ended up with trash as a result.
If you had negated 11.1000(2) as appropriate for signed-binary, you'd end up with 01.1000(2) -- the correct answer.
If you had started with the 2's complement representation of -1.5, 10.1000(2), and took the 2's complement of that, you'd end up with 01.1000(2) -- also correct.
Note that none of this involves converting anything to decimal.
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.
Let's say I have the two's complement form of the hexadecimal A41B and I want to convert it to decimal. Normally, I would convert it to binary, flip all the bits, add one, and then convert it to decimal and put the correct sign (positive or negative). Is there a faster way to do this by hand?
You can:
convert it to decimal
subtract 2N from the result, where N is your word size (eg. for 16-bit words, subtract 65536)
In your example,
0xA41B = 42011
42011 - 65536 = -23525
Before doing the subtraction, you would check that the sign bit is in fact 1. Otherwise you would simply have a positive number.
From dave's corner:
=MOD(HEX2DEC(A7)+2^15,2^16)-2^15
for 16 bit numbers.
If you for some reason don't want to or can't perform the subtraction that the other answers suggest, you can treat negative numbers like this:
Flip the bits
Add one
Convert to decimal as if the number were positive
Add a negative sign
For example: -5 is 11111011 in 8-bit 2's complement. Flipping the bits and adding one is 00000101, which is 5 in decimal. Add negative sign and you have -5.
Please move this question to other stackexchange site if its not the part of SO.
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