Electronics and Communication Engineering - Digital Electronics - Discussion

7. 

In 2's complement representation the number 11100101 represents the decimal number

[A]. +37
[B]. -31
[C]. +27
[D]. -27

Answer: Option D

Explanation:

A = 11100101. Therefore A = 00011010 and A' = A + 1 = 00011011 = 16 + 8 + 2 + 1 = 27. Therefore A = -27.


Siddiq said: (Jul 15, 2014)  
Why -ve sign?

Sangeetha said: (Jul 17, 2014)  
The first no 1 indicates the -ve number.

Eshwar said: (Jul 19, 2014)  
Yes the first num indicates the negative number so the two 's complement must be a positive number right.

Anuradha said: (Sep 10, 2014)  
I don't understand this step - 00011011 = 16 + 8 + 2 + 1 = 27. Therefore A = -27.

Derepika said: (Sep 16, 2014)  
How 16+8+2+1 comes from 00011011 in hexadecimal.

Jitendra said: (Oct 14, 2014)  
-ve sign is problem here.

According to first no. it should be +ve.

Rajesh Shakya said: (Nov 1, 2014)  
How can decide fist bit (sign bit or MSB)?

Suman said: (Dec 15, 2014)  
How we can we get 16+8+2+1?

Akash Choudhary said: (Dec 22, 2014)  
In 2's complement if first digit from left is 1 then it is a -ve number else 0 then +ve number.

Santhoshstebin said: (Jan 21, 2015)  
0 mean positive value 1.
1 mean negative value -1.

Naina said: (Jan 21, 2015)  
I don't understand this step 16+8+2+1.

Sudha said: (Jan 31, 2015)  
00011011 = 00011011.

= 0(2^7)+0(2^6 )+0(2^5)+1(2^4 )+1(2^3)+0(2^2)+1(2^1)+1(2^0).

= 16+8+2+1 = -27.

Sai said: (Apr 16, 2015)  
Given A = 11100101.

2's comp A' = A + 1 = 00011011.

Why did you consider from A? Why didn't you consider from A' I mean sign.

Ashok said: (Jun 17, 2015)  
I don't understand 16+8+2+1.

Geetha Adainjan said: (Jul 1, 2015)  
2's com -11100101. Then 1's com is 11100101-1=1100100.

Then the required binary no is 0011011. According to binary to decimal conversion the position value is 128, 64, 32, 16, 8, 4, 2, 1 here binary 1 is present in 16+8+2+1=27.

E&Amp;Tc Group D.Y. Patil Ambi Pune said: (Jul 16, 2015)  
-(2^4=16, 2^3=8, 2^1=2, 2^0=1) = -27.

Anshika said: (Oct 22, 2015)  
How come it is -ve sign. It should be +ve?

Can anyone explain me?

B.Mallesh Goud said: (Nov 26, 2015)  
Why we use -ve sign instead of +ve sign?

Sita said: (Dec 24, 2015)  
In the given binary form msb bit is 1 should keep '-' sign. Msb bit is 0 then you should keep positive sign.

Aslam said: (Jan 5, 2016)  
They asked decimal equivalent of 2's complement of 11100101 which is 00011011 here MSB is 0, hence +27.

Vishal said: (Jan 24, 2016)  
Yes @Aslam its +27.

Renu said: (Jun 30, 2016)  
How did you get - symbol. Please explain clearly.

Priyanka said: (Jul 28, 2016)  
I think this negative sign has been confirmed from the MSB and LSB bits of the given number and not the 1's complement number.

After finding answer through the appropriate orocedure as discuss above, check the given number, and give the particilar +ve or -ve sign to the answer. Thats it.

Ramakrishna said: (Aug 5, 2016)  
2's compliment represent of any number is - (2's compliment of the original number).

Lovish said: (Aug 15, 2016)  
It should be positive.

Rahul said: (Sep 24, 2016)  
The negative number always represent in 2's complement form. So after calculating 2's complement of the above binary number, it is always negative. So the D option is correct.

Arun said: (Oct 1, 2016)  
There is no carry bit. If the carry bit present it will be positive or else it will be negative.

Zain said: (Oct 12, 2016)  
It should be +27.

Arindom said: (Oct 22, 2016)  
Iy should be +27 because the msb obtain after the calculation is 0 which indicates its sign bit as +ve.

Harish Johnty said: (Nov 25, 2016)  
Here they just asked that 2's compliment of the decimal number is 11100101 so what is that decimal number?

If you see MSBbit is one so the decimal number should be in negative not positive.

Vishesh Kumar said: (Mar 7, 2017)  
The correct answer is +27.
i.e option D.

Selvamani Kannan said: (Mar 17, 2017)  
For a two's compliment, we add +1 with the ones compliment.

So, from two's compliment to one's compliment we have to subtract -1.

I think +27 is correct.

Satish said: (Mar 31, 2017)  
The Correct option is +27.

Pradeep said: (May 14, 2017)  
I agree with the given answer -27.

Aditya Gupta said: (Jun 14, 2017)  
It is used in short form that you are seeing 16+8+2+1. It is basically the conversion of binary in decimal where 1 is there we add all that positions by taking 2^4+2^8+2^1+2^0 power here represents the position of bits.

Uday Kumar said: (Aug 17, 2017)  
Why negative sign comes?

Prakash Kasera said: (Sep 14, 2017)  
Please understand the question?
The question is saying that the given binary number 11100101 is in already 2's complement form, then how can we write 11100101 in decimal format?

Ans: Left most digit is 1 means it should be a negative number (A/C to question)
1= -ve
0= +ve

step_1------->substract 1 from 11100101 to get 1's complement form
we will get 1's form = 11100100.

step_2--------> Now reverse each digit of 11100100 to get original number in binary
we will get 00011011=27.

step_3--------> so answer will be -27.

Nikhil said: (Sep 14, 2017)  
Msb bit decides the sign of the number. After finding the 2's compliment the msb bit is 0, hence the negative sign. If it was 1 it would hav been +27.

Abarna said: (Oct 12, 2017)  
How to convert a signed binary two's complement?
1110 0101(2) to an integer in decimal system (in base 10)

1. Is this a positive or a negative number?
In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.
1110 0101 is the binary representation of a negative integer, on 8 bits.


2. Get the binary representation in one's complement:
* Run this step only if the number is negative *
Subtract 1 from the binary initial number:
1110 0101 - 1 = 1110 0100


2. Get the binary representation of the positive (unsigned) number:
* Run this step only if the number is negative *
Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1110 0100) = 0001 1011


3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

27
0
26
0
25
0
24
1
23
1
22
0
21
1
20
1

4. Multiply each bit by its corresponding power of 2 and add all the terms up:
0001 1011(2) = (0 * 27 + 0 * 26 + 0 * 25 + 1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20)(10) = (0 + 0 + 0 + 16 + 8 + 0 + 2 + 1)(10) = (16 + 8 + 2 + 1)(10) = 27(10).

5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1110 0101(2) = -27(10).

Raj said: (Nov 5, 2017)  
At all many have a doubt for the negative sign doubt so I ll try to solve it.

In digital electronics the MSB bit (the leftmost bit) is the sign bit and its negative if it is set to 1 or if it is set to 0 it is positive. So look at the MSB perform the operation and represent it as positive or negative depending on the sign bit.

Sneha said: (Nov 13, 2017)  
If carry is generated find 2's complement of the answer to get final result,

If carry is not generated give negative sign and write the value.

Priyajit Pal said: (Dec 18, 2017)  
Negative numbers are always represented in 2's compliment form. That's why the original no must be negative.

Veer said: (Jul 14, 2018)  
How it comes in negative.

Mannu Jha said: (Jul 21, 2018)  
The MSB holds the sign.

Basava Prabhu said: (Jul 25, 2018)  
2's complement means only negitive number. If we take 2's complement of 011 then it means negitive of 011.

Aparna said: (Jul 28, 2018)  
I can't understand it clearly, Please give me the explanation in detail.

Muthupandi said: (Dec 21, 2018)  
I am not getting this, please anyone explain me.

Abhishek B Revankar said: (Aug 4, 2019)  
Carry 1 indicates a positive number.
Carry 0 indicates a negative number.
Hence after adding 1 to the complement, the carry remains 0.

Anonymous said: (Nov 20, 2019)  
Explanation and answer are wrong.

Number with Most Significant digital represents a negative number i.e.
-1*128+1*64+1*32+0*16+0*8+1*4+0*2+1*1.
=-128+64+32+4+1=-27 (which is original number).

Now, 2's complement of the number will be:
1's C: 00011010.
2's C: 00011011.

Binary Equivalent: 16+8+2+1=27 (which is required answer).

Anubhav Dandapat said: (May 11, 2020)  
Is the 1's complement and 2's complement are the complement each other?

Because the procedure is same, if we find the 2's complement we use the same procedure and here also use the same procedure.

Chandu said: (Aug 18, 2020)  
I think in any condition the 1st bit indicates sign of that number and 0 indicates positive sign and 1 indicates negative sign.

Selva Ganesh.V said: (Nov 26, 2020)  
A = 11100101.
Therefore A = 00011010 and A' = A + 1 = 00011011 = 16 + 8 + 2 + 1 = 27.
Therefore A = -27.

Akhilesh Prajapati said: (Jun 15, 2021)  
The Answers Should be C.

Maham Fayyaz said: (Aug 22, 2021)  
Negative signed indicates the signed Binary numbers as we take compliment of only -ve signed numbers.

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