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Answer:

 First note that the "sign bit" is set, so the integer is negative.
 Then find the positive integer:
 1001 1111    reflect    0110 0000    add one   0110 0001
convert to decimal 26 +25 + 1 = 9710
put sign in front -9710

Overflow Detection in 2's Complement

The binary addition algorithm can be applied to any pair of bit patterns. The electronics inside the microprocessor performs this operation with any two bit patterns you send it. You send it bit patterns. It does its job. It is up to you (as the writer of the program) to be sure that the operation makes sense.

Overflow is detected in a different way for each representation scheme. In the following exhibit the "binary addition algorithm" is applied to two bit patterns. Then the results are looked at as unsigned binary and then as two's complement:

Algorithm applied to
bit patterns
Interpretation of the patterns
as unsigned binary
(shown in base 10)
Interpretation of the patterns
as 2's complement
(shown in base 10)
carry bits in blue patterns as decimal patterns as decimal

The "binary addition algorithm" was performed on the operands. The result is either correct or incorrect depending on how the bit patterns are interpreted. If the bit patterns are regarded as unsigned binary integers, then overflow happened. If the bit patterns are regarded as two's comp integers, then the result is correct.

Correct Two's Complement Addition

When the "binary addition algorithm" is used with operands in two's complement representation:

The result is correct if the carry INTO the high order column equals the carry OUT OF the high order column.

The carry bits can both be zero or both be one.


QUESTION 23:

If the bit patterns in the above addition problem are regarded as two's complement, is the result correct?