Barrel shifter

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A barrel shifter is a

.

For example, take a four-bit barrel shifter, with inputs A, B, C and D. The shifter can cycle the order of the bits ABCD as DABC, CDAB, or BCDA; in this case, no bits are lost. That is, it can shift all of the outputs up to three positions to the right (and thus make any cyclic combination of A, B, C and D). The barrel shifter has a variety of applications, including being a useful component in microprocessors (alongside the ALU).

Implementation

The very fastest shifters are implemented as full crossbars, in a manner similar to the 4-bit shifter depicted above, only larger. These incur the least delay, with the output always a single gate delay behind the input to be shifted (after allowing the small time needed for the shift count decoder to settle; this penalty, however, is only incurred when the shift count changes). These crossbar shifters require however n² gates for n-bit shifts. Because of this, the barrel shifter is often implemented as a cascade of parallel 2×1 multiplexers instead, which allows a large reduction in gate count, now growing only with n x log n; the propagation delay is however larger, growing with log n (instead of being constant as with the crossbar shifter).

For an 8-bit barrel shifter, two intermediate signals are used which shifts by four and two bits, or passes the same data, based on the value of S[2] and S[1]. This signal is then shifted by another multiplexer, which is controlled by S[0]:

 int1  = IN       , if S[2] == 0
       = IN   << 4, if S[2] == 1
 int2  = int1     , if S[1] == 0
       = int1 << 2, if S[1] == 1
 OUT   = int2     , if S[0] == 0
       = int2 << 1, if S[0] == 1

Larger barrel shifters have additional stages.

The cascaded shifter has the further advantage over the full crossbar shifter of not requiring any decoding logic for the shift count.

Cost

The number of multiplexers required for an n-bit word is ${\displaystyle n\log _{2}n}$.

and the number of multiplexers needed are listed below:

• 128-bit — ${\displaystyle 128\times \log _{2}128=128\times 7=896}$
• 64-bit — ${\displaystyle 64\times \log _{2}64=64\times 6=384}$
• 32-bit — ${\displaystyle 32\times \log _{2}32=32\times 5=160}$
• 16-bit — ${\displaystyle 16\times \log _{2}16=16\times 4=64}$
• 8-bit — ${\displaystyle 8\times \log _{2}8=8\times 3=24}$

Cost of critical path in FO4 (estimated, without wire delay):

• 32-bit: from 18 FO4 to 14 FO4^[3]

Uses

A common usage of a barrel shifter is in the hardware implementation of

, until it matches the exponent of the larger number. This is done by subtracting the exponents and using the barrel shifter to shift the smaller number to the right by the difference, in one cycle.

See also

• Circular shift

References

Further reading

• Kroening, Daniel; Strichman, Ofer (2008). Decision Procedures.
  ISBN 978-3-540-74104-6
  .

External links

• Barrel-shifter (8 bit), University of Hamburg
• Implementing Barrel Shifters Using Multipliers (Paul Gigliotti, 2004-08-17)