Question

When we looked at multiplication of signed operands, we saw in the class slides an example of multiplication of a positive multiplicand and a positive multiplier, and a negative multiplicand and a positive multiplier. Perform the multiplication algorithm which we described, using left shifting of a copy of the multiplicand, and addition, to determine whether it gives the correct result for the following examples, using 4 bit operands and a 4 bit result, and show all steps in performance of the algorithm, and then answer the four accompanying questions after each problem: a. Positive multiplicand and negative multiplier (3 * -2) i. Should the result fit in 4 bits? ii. Is the correct result produced? iii. Is there overflow from any of the addition operations (you can simply say if there is overflow from any one or more of them)? iv. If there is overflow from any of the addition operations, does this make sense? Why or why not? b. Negative multiplicand and negative multiplier (-3 * -2) i. Should the result fit in 4 bits? ii. Is the correct result produced? iii. Is there overflow from any of the addition operations (you can simply say if there is overflow from any one or more of them)? iv. If there is overflow from any of the addition operations, does this make sense? Why or why not?

Answer 1

Multiplicand = 3, multiplier = 2 The result obtained is phi = 0110 = 6 i) result will not fit in 4 bits an extra sign bit is required to hold the sign ii) The magnitude of the results is correct but not the sign iii) there is an overflow occurred in the second addition iv) yes the overflow results in the elimination of the negative sign. B) multiplicand = -3, multiplier = -2 The result obtained is = 0110 = 6 i) Result will not fit in the 4 bits ii) Result is correct iii) There is no addition overflow iv) No there is no overflow occurred