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ISRO2013-ECE 2s compliment number

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The two numbers represented in signed $\text{2s}$ complement form are $\text{P}= 11101101$ and $\text{Q}= 11100110.$ If $\text{Q}$ is subtracted from $\text{P},$ the value obtained in signed $\text{2s}$ complement form is: 

  1. $1000001111$
  2. $00000111$
  3. $11111001$
  4. $111111001$
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Ans.b) 0000 0111

The most significant bit is 1 in P and Q, so the both represents a negative value

P= 1110 1101= (-19)10

Q= 1110 0110= (-26)10

P-Q=(-19) - (-26) = -19 + 26 = 7 =(0000 0111)2

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P = 11101101

Q = 11100110

P-Q = P+(-Q) [Here (-Q) means 2's complement of Q]

So, 2's complement of Q = 0001 1001 + 1 = 0001 1010

Now P + Q = 1110 1101 + 0001 1010 = 0000 0111

Answer is option (b)
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