VLSI Digital Signal Processing Systems: Design and Implementation

14.9    PROBLEMS

1. Consider the hybrid addition of a carry-save unsigned number X and an unsigned conventional number Y. Similar to the hybrid radix-2 redundant addition discussed in Section 14.3.1, the first step of this addition is computed as :

   

   (a)   Let and Design a parallel adder similar to the hybrid adder in Fig. 14.1 for a wordlength of 8. Specify appropriate encoding of t_i and u_i.

   (b)   Design the corresponding msd-first and lsd-first serial architectures.

2. The adder in Fig. 14.5 computes S_<2,1> = (X_<2,1> + Y ⁺) – Y ⁻. Redesign another possible redundant adder architecture for the addition computation using S_<2,1> = (X_<2,1> – Y ⁻) + Y ⁺ in

   (a)    digit-parallel,

   (b)    lsd-first digit-serial, and

   

   Fig. 14.23    Block diagram of msd-first redundant to nonredundant converter.

   

   Fig. 14.24    Msd-first redundant to nonredundant converter.

   (c)    msd-first digit-serial

   implementation styles.

3. Design the msd-first and lsd-first serial architectures for the addition of 2 carry-save numbers. ...