what is the 2's complement representation of -14 using 5 bits?

Question

i ned to understand how the 2's complement works and how to deal with it. 

Answer 1

Twos Complement is an operation on a Binary number.

   (You could have a threes complement on a base 3 number etc.)

 

Twos Complement is the way computers subtract numbers.

To subtract A from B you take the Twos Complement of A and Add it to B.

Negative numbers are represented by the two's complement of the positive number.

 

Here is how you do a Twos Complement:

Write out the binary number.

Invert each digit. (0=>1, 1=>0)

Then do a binary addition of one to that result.

 

3 is 11 in binary (in 2 bit representation)
invert it => 00
now add 1 => 01
so 01 is the Twos Complement of 3 (or a -3 that would be added to another number)

 

3 is 0011 in binary (in 4 bit representation)

invert it => 1100

now add 1 => 1101

so 1101 is the Twos Complement of 3 (or a -3 that would be added to another number)

 

10 is 1010 in binary

invert it => 0101

add 1 => 0110

so 0110 represents a negative 10

 

Now the answer to your question depends.

Does your professor want you to find the 2's complement of 14

   so that you could then add it to another number thereby

   subtracting 14 from that other number?   e.g. 23 +(-14)

OR does your professor want you to find the 2's complement of -14

   so that you could then add it to another number thereby

   subtracting a -14 from another number   e.g.  23 +(-(-14))

 

I will assume that you are trying to subtract 14 from some other number

So 14  is  1110  in binary  (or using 5 bits 01110)

invert it => 10001

add 1  => 10010

So 10010  is 2's complement of 14 and you could send that binary number along with another number X into an adder circuit to subtract 14 from X.