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.
Related
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
So i was told that two's complement is usually to used to find complement of a number and I used it only to complement positive numbers (i.e positve --> negative conversion) however I just got an example in book which asks me the following :
Express 23, -23, and -9 in 8-bit binary two’s Complement
form
now what does that mean? 23 means -23 in binary and -23 means 23 ?
sorta confused over there
2's complement is used to represent negative numbers, which in turn, can be used to do subtraction.
23 = 00010111b
To get -23 (2's complement of 23), flip all the bits, and add 1:
11101000b + 1
=11101001b (-23)
-9 is the 2's complement of 9. 9 is
00001001b
So -9 is
11110111b (Flipping and add +1)
See also here
The representation of positive numbers in 2's complement is same as the unsigned representation. Things start to change when negative representation comes into play. So, in general, for given w bits, the numbers that can be represented in 2's complement are -2^(w-1)-1 to 2^(w-1) with the w bit being the signed bit. So since you have 8 bits you can represent numbers from -128 to 127. The 8th bit will be the signed bit, with 0 being positive and 1 representing negative.
For any positive representation of a number in binary 2's complement N the negative counterpart -N is pretty simple to find, just invert the bits, and add one. Example:
7 in 2's complement is 0111, inverting these bits gives: 1000, adding one gives 1001, which is -7 in 2's complement! Hope this helps!
So this was one of the questions in my textbooks, we haven't got there yet but i'm interested in how this all works,
For the first bit here, my understanding of one's complement is you flip so where there are 1's you put 0's and 0's you put ones. This has to be 8 bit so i added a zero to the binary at the start
Therefre 01001001
Write down the following binary representations of +73:
8-bit unsigned: 01001001
8-bit signed-magnitude: 01001001
8-bit one's complement: 10110110
8-bit two's complement: 10110111
8-bit excess-128: 10110111
These are the answers I came up with, but i'm fairly certain i did them wrongly. Any clarification on this?
Secondly, how the heck to I do it with a negative so -73, the binary is just -01001001 so I assume that is the signed, do you do the same technique as above( assuming i have got them correct)
8-bit signed-magnitude: -01001001
8-bit one's complement:
8-bit two's complement:
8-bit excess-128:
Thanks in advance for any help
+73 is 01001001 in all the representations you named except excess-128. In excess-128 its 11001001 (add 128 to it). Sign magnitude, one's complement, and two's complement are all the same for positive numbers and only differ for negative numbers. The value of -73 in those representations is:
8-bit sign magnitude 11001001
8-bit one's complement 10110110
8-bit two's complement 10110111
8-bit excess-128 00110111
the one's complement 'flip all bits' is how you negate a number in one's complement notation. So if you have n, to get -n you flip all the bits.
'flip all bits and add 1' is how you negate a number in two's complement.
Both one's complement and two's complement have one odd value. For one's complement that's -0 (all bits set), which is really the same as 0 -- or you can treat it as invalid and special case negating 0. For two's complement, that's -2^(n-1) -- -128 for 8-bit -- which is a number that negates to itself due to overflow.
What is the advantage of 2's complement over 1's complement in negative number representation in binary number system? How does it affect the range of values stored in a certain bit representation of number in binary system?
The primary advantage of two's complement over one's complement is that two's complement only has one value for zero. One's complement has a "positive" zero and a "negative" zero.
Next, to add numbers using one's complement you have to first do binary addition, then add in an end-around carry value.
Two's complement has only one value for zero, and doesn't require carry values.
You also asked how the range of values stored are affected. Consider an eight-bit integer value, the following are your minimum and maximum values:
Notation Min Max
========== ==== ====
Unsigned: 0 255
One's Comp: -127 +127
Two's Comp: -128 +127
References:
http://en.wikipedia.org/wiki/Signed_number_representations
http://en.wikipedia.org/wiki/Ones%27_complement
http://en.wikipedia.org/wiki/Two%27s_complement
The major advantages are:
In 1's there is a -0 (11111111) and a +0 (00000000), i.e two value for the same 0. On the other hand, in 2's complement, there is only one value for 0 (00000000). This is because
+0 --> 00000000
and
-0 --> 00000000 --> 11111111 + 1 --> 00000000
While doing arithmetic operations like addition or subtraction using 1's, we have to add an extra carry bit, i.e 1 to the result to get the correct answer, e.g.:
+1(00000001)
+
-1(11111110)
-----------------
= (11111111)
but the correct answer is 0. In order to get 0 we have to add a carry
bit 1 to the result (11111111 + 1 = 00000000).
In 2's complement, the result doesn't have to be modified:
+1(00000001)
+
-1(11111111)
-----------------
= 1 00000000
Negative integers :
2's complement makes sense to be used for negative integers. 1's complement is just a computation technique which might be helpful to evaluate 2's complement. The real (defeated) rival of 2's complement was the sign-magnitude representation for negative integers.
No overflow : 1's complement has no special usage for negative integers. 2's complement makes sense because it can be used in natural addition and subtraction arithmetic without any need to change the bits. Providing that no overflow occurs, the sign bit of the result is just the right value. The bit number promotion in this notation is straight forward, for example, to promote an 8-bit signed integer to 16, we could simply repeat the sign bit of integer value in the high byte of it.
Sign magnitude : On the contrary, the sign-magnitude notation is just the way that human uses to represent negative integers. The bit number promotion and addition subtraction arithmetic is a bit mess with this notation.
Advantages of Two’s Complement #1
In Two’s Complement representation, the value zero is
uniquely represented by having all bits set to zero:
**
Advantages of Two’s Complement #2
**
When you perform an arithmetic operation (for example,
addition, subtraction, multiplication, division) on two
signed integers in Two’s Complement representation, you
can use
exactly the same method
as if you had two
unsigned integers (that is, nonnegative integers with no sign
bit) ...
EXCEPT
, you throw away the high carry (or the high
borrow
for subtraction)
Advantages of Two’s Complement #3
This property of Two’s Complement representation is so
incredibly handy that virtually every general
purpose
computer available today uses Two’s Complement.
Why? Because, with Two’s Complement, we don’t need
special algorithms
(and therefore extra circuitry) for
arithmetic operations that involve negative values.
Another major advantage of Two's complement over signed bit representation is 2's complement representation is easy to manipulate in hardware
2s complement isn't for representing a negative number it's an inverse.
Means you can do A + B' (where B' is the 2s complement of B) to give A - B, means you can do everything with an adder and not need a substracter