Advanced Digital Logic Design

Chapter08 - Home
Exercises: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20

Exercise. This is the solution to exercise 8.1 in the book.

Solution. If using signed number notation then multiplication of two n-bit numbers is effectively the multiplication of two unsigned (n-1)-bit numbers and ”multiplication” of the sign bits. This means that the absolute range of the product is reduced to 2n-2 bits. Using 2’s complement notation not only is the range of the multiplier and multiplicand greater by one, but also the absolute range of the product is greater. Moreover, most implementations use 2’s complement so using a signed notation multiplier means first translating the multiplier and multiplicand from 2’s complement to signed bit notation, then effecting the multiplication, then translating the product back from signed number notation to 2’s complement.