Step-by-step Solution:

Convert both numbers to decimal (two’s complement form) \[ A = 10011001_2 \] MSB = 1 ⇒ negative number Invert bits: \[ 01100110_2 = 102_{10} \] Add 1: \[ 102 + 1 = 103 \] \[ \Rightarrow A = -103 \] \[ B = 11010111_2 \] MSB = 1 ⇒ negative number Invert bits: \[ 00101000_2 = 40_{10} \] Add 1: \[ 40 + 1 = 41 \] \[ \Rightarrow B = -41 \] Add them \[ A + B = -103 + (-41) = -144 \] In 8-bit two’s complement, range is: \[ -128 \text{ to } +127 \] Since \[ -144 < -128 \] \[ \Rightarrow \textbf{Overflow occurs} \] Compute the 8-bit result (binary addition) \[ 10011001 \] \[ +11010111 \] \[ = 1,01110000 \quad (9 \text{ bits}) \] Drop the carry beyond 8 bits: \[ 01110000 \] Final Result \[ {01110000_2} \] Overflow occurred.
Actual mathematical result = (-144),
Stored 8-bit value = (+112).