Correct : b,d

In 4-bit two''s complement the representable range is −8 to +7. Overflow occurs when two numbers of the same sign are added and the result falls outside this range — detected when the carry into the MSB differs from the carry out of the MSB.
First converting all four numbers — N1 = 1011 = −5, N2 = 1101 = −3, N3 = 1010 = −6, N4 = 1001 = −7.
Option A — N1 + N2 = −5 + (−3) = −8
1011 + 1101 = 11000. The 4-bit result is 1000 = −8, which is within range. Carry into MSB = 1 and carry out = 1 are equal. No overflow.
Option B — N2 + N3 = −3 + (−6) = −9
1101 + 1010 = 10111. The 4-bit result is 0111 = +7, but both operands were negative. The result changed sign — overflow. Carry into MSB = 1, carry out = 0, they differ. Overflow occurs.
Option C — N3 − N4 = −6 − (−7) = +1
Subtracting N4 means adding its two''s complement. Two''s complement of 1001 is 0111 = +7. So 1010 + 0111 = 10001. The 4-bit result is 0001 = +1, within range. No overflow.
Option D — N1 + N4 = −5 + (−7) = −12
1011 + 1001 = 10100. The 4-bit result is 0100 = +4, but both operands were negative. Sign changed — overflow. Carry into MSB = 0, carry out = 1, they differ. Overflow occurs.
Correct answer: B and D ✓