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 :

    image

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

    (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

    image

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

    image

    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. ...

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