UGC NET CSE | July 2018 | Part 2 | Question: 96

Question

Perform the following operation for the binary equivalent of the decimal numbers $(-14)_{10}+(-15)_{10}$. The solution in 8 bit representation is

• A. 11100011
• B. 00011101
• C. 10011101
• D. 11110011

Comments

if u perform addition in sign magnitude form then option 3

but generally we use 2's complement representation hence 1 is right

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yes we use 2's complemnt form.to store -ve numbers due to its correctness..!

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i think ans is B ? if i wrong then correct me

Answer 1

To add 2 negative binary numbers, change them into 2's complement form, and then add it.
So in this case,

• $-(14)_{10}$ = $00001110_2$ 
• $-(15)_{10}$ =$00001111_2$

2's complement of $(00001110)_2 \longrightarrow  11110001+1 = 11110010$
2's complement of $(00001111)_2 \longrightarrow 11110000+1 = 11110001$

add them to get the solution:

$(11110010)_2$ + $(11110001)_2= (11100011)_2$

Option $(A)$ is correct.

Answer 2

By default we use 2's complement representation.

 

Answer 3

Option A 11100011
 

(−14)₁₀+(−15)₁₀  

(−29)₁₀ 

=    1        1     1      0    0    0   1   1
   -128    64    32    16   8   4   2   1