Lookahead carry unit

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A lookahead carry unit (LCU) is a logical unit in digital circuit design used to decrease calculation time in adder units and used in conjunction with carry look-ahead adders (CLAs).

4-bit adder

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A single 4-bit CLA is shown below:

 
4-bit adder with Carry Look Ahead (CLA)

16-bit adder

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By combining four 4-bit CLAs, a 16-bit adder can be created but additional logic is needed in the form of an LCU.

The LCU accepts the group propagate ( ) and group generate ( ) from each of the four CLAs.   and   have the following expressions for each CLA adder:[1]

 
 

The LCU then generates the carry input for each CLA.

Assume that   is   and   is   from the ith CLA then the output carry bits are

 
 
 
 

Substituting   into  , then   into  , then   into   yields the expanded equations:

 
 
 
 

  corresponds to the carry input into the second CLA;   to the third CLA;   to the fourth CLA; and   to overflow carry bit.

In addition, the LCU can calculate its own propagate and generate:

 
 
 
 
16-bit adder with LCU

64-bit adder

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By combining 4 CLAs and an LCU together creates a 16-bit adder. Four of these units can be combined to form a 64-bit adder. An additional (second-level) LCU is needed that accepts the propagate ( ) and generate ( ) from each LCU and the four carry outputs generated by the second-level LCU are fed into the first-level LCUs.

 
64-bit adders with a second-level LCU

References

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  1. ^ "Carry Look Ahead Adder". Archived from the original on 2011-09-25. Retrieved 2011-10-07.