Question

A shift operation is often used to implement either multiply-by-power-of-2 or divide-by power-of-2 operations. For example, 0010 x4 1000. This multiplication can be achieved by shifting 0010 by 2 bits to the left. Likewise, 10004 0010, which can be obtained by shifting 1000 to the right by 2 bits. As multipliers are more "expensive" in terms of area and power consumption, multiplication by shifting is preferred if applicable. Sometime, the multiplier does not have to be power-of-2. For example, 0010 x 5 0010 x (4+1) 0010x 4 + 0010-1010. This result can be obtained by first shifting 0010 to the left by 2 bits and then adding the result with 0010. Shift and add operation may still be less expensive than multiplication in many applications. One problem of the shifter is that it may take different clock cycles for different amount of shifting. For example, it takes 6 cycles to shift a word by 6 bits to the left while it takes 1 cycle to shift it by 1 bit. By using MUXes as in Example 28-4, one can design a shift register that requires same amount of time, i.e., 1 cycle, to shift however many bits to the left or right. This type of shift register is called barrel shifter, and is used in many computation-intensive applications such as DSP (Digital Signal Processing). For example, a 4-bit barrel shifter (left only) may be designed by adding a 4-to-1 MUX to.each D flip- flop. The shift amount C,Co is connected to the control inputs of the MUX. Data inputs lo, Ii, l', 1, are then connected to the output of the current flip-flop, immediate right flip-flop, and so forth. The reader is encouraged to design a simple barrel shifter in the following exercise. 28-2: Show how the following operations may be performed by shifting and adding/subtracting only 1。15 × 5 2. 16:8 3. 15 x 10

Answer 1

1111₂ means number in binary

15₁₀ means number in decimal system

15X5 15іо- , 111, in Binary 5 lol in Binr )-1001011 111100 t ID here multipication Lebt 2 bita Lo to 3 brlb to Right. by ti, 6 1o

ら15% 10 15, 1111 10 2 15 x 10ニ 1111 x lolo-1111-(1000 + lo IM Um 15 x )o 1111000 + 11110-100lo110 150 120+3o 10 1o lo 15o