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Write short note on look ahead carry adders.

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By Dipali Umre

  1. A Carry Look Ahead adder (CLA) or fast adder is a type of adder used in digital logic.
  2. A carry look ahead adder improves speed by reducing the amount of time required to determine carry bits.
  3. The carry look ahead adder calculates one or more carry bits before the sum, which reduces the waiting time to calculate the result of the larger value bits of the adder.
  4. Carry look ahead depends on two things :
    a. Calculating for each digit position whether that position is going to propagate a carry if one comes in from the right.
    b. Combining these calculated values to be able to deduce quickly whether, for each group of digits, that group is going to propagate a carry that comes in from the right.
  5. Carry look ahead logic uses the concepts of generating and propagating carries.
  6. The addition of two binary numbers in parallel implies that all the bits of the augend and addend are available for computation at the same time.
  7. The carry propagation time is an important attribute of the adder because it limits the speed with which two numbers are added.
  8. A solution is to increase the complexity of the equipment in such a way that the carry delay time is reduced.

Pi= Ai ⊕ Bi, Gi= AiBi

The output sum and carry can respectively be expressed as,

Si = Pi⊕Ci, Ci+1= Gi + PiCi

is called a carry generate, and it produces a carry of 1 when both Ai and Bi are 1, regardless of the input carry Ci. Pi is called a carry propagate, because it determines whether a carry into stage i will propagate in stage i + 1

C0 = input carry

C1 = G0 + P0C0

C2 = G1 + P1C1 = G1 + P1(G0 + P0C0) = G1 + P1G0 + P0P1C0

C3 = G2 + P2C2 = G2 + P2G1 + P2P1G0 + P2P1P0C0

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