Let's consider these occurrences now. Obviously both of these results are incorrect, but in this case overflow is harder to detect. Adding fractions There is no further difficult in adding two signed fractions , only the interpretation of the results differs. If you look carefully at these examples, you'll see that the binary representation and calculations are the same as before , only the decimal representation has changed. This is very useful because it means we can use the same circuitry for addition, regardless of the interpretation of the results.
Multiplication Multiplying unsigned numbers Multiplying unsigned numbers in binary is quite easy.
Recall that with 4 bit numbers we can represent numbers from 0 to 15. In this case the result was 7 bit, which can be extended to 8 bits by adding a 0 at the left. When multiplying larger numbers, the result will be 8 bits, with the leftmost set to 1, as shown. There are many methods to multiply 2's complement numbers. The easiest is to simply find the magnitude of the two multiplicands, multiply these together, and then use the original sign bits to determine the sign of the result.