5.2.4 Carry Skip Adder As A Carry Skip Adder
5.2.4 Carry Skip Adder
A carry-skip adder (also known as a carry-bypass adder) is an adder implementation that improves on the delay of a ripple-carry adder. The two addends are split in blocks of n bits. The output carry of each block is dependent on the input carry only if, for each of the n bits in the block, at least one addend has a 1 bit (see the definition of carry propagation at Carry-look ahead adder). The output carry Coi+n-1, for the block corresponding to bits i to i+n-1 is obtained from a multiplexer, wired as follows:
SEL = (Ai + Bi) (Ai+1 + Bi+1) ….. (Ai+n-1 + Bi+n-1) A = Cripple, i+n-1 (the carry output for the ripple adder summing bits i to i+n-1) B = Cout, i-1.
This greatly reduces …show more content…
In this case, the RCA is as slow as it is large. Actually, RCA are fast only for some configurations of the input words, where carry signals are generated at some positions. Depending on the position at which a carry signal has been generated, the propagation time can be variable. Carry Skip Adders take advantage both of the generation or the propagation of the carry signal. They are divided into blocks, where a special circuit detects quickly if all the bits to be added are different (Pi = 1 in the entire block). The signal produced by this circuit will be called block propagation signal. If the carry is propagated at all positions in the block, then the carry signal entering into the block can directly bypass it and so be transmitted through a multiplexer to the next block. As soon as the carry signal is transmitted to a block, it starts to propagate through the block, as if it had been generated at the beginning of the block. Figure 5 shows the structure of a 16-bits skip carry adder, divided into 2, 4 and 8-blocks. It becomes now obvious that there exist a trade-off between the speed …show more content…
ak+1 ak+2 ak 010101 al+2 al+1 al …….
….. bk+1 bk+2 bk 101010 bl+2 bl+1 bl …….
If Cl+3 = 1 then carry will propagate to position k; to speed-up operation, propagation is skipped to position i without waiting for rippling operation time varies according to operands as in carry-complete addition to implement carry-skip adder, stages are divided into blocks and carry-skip logic is added to each block to detect when carry-in the block can be passed directly to the next block define carry transfer Ti = ai + bi carry skipping can be detected for a block size of m as follows (carry propagates through all stages): Tj . Tj+1…….Tj+m-1 = 1 ( = (aj + bj) . (aj+1 + bj+1) …. ) note: this takes into account both propagated and generated carries!
Carry out from the block (m-bits in a block) is Tj . Tj+1 …. Tj+m-1 . Cj + Cj+m Skipped
A carry-skip adder (also known as a carry-bypass adder) is an adder implementation that improves on the delay of a ripple-carry adder. The two addends are split in blocks of n bits. The output carry of each block is dependent on the input carry only if, for each of the n bits in the block, at least one addend has a 1 bit (see the definition of carry propagation at Carry-look ahead adder). The output carry Coi+n-1, for the block corresponding to bits i to i+n-1 is obtained from a multiplexer, wired as follows:
SEL = (Ai + Bi) (Ai+1 + Bi+1) ….. (Ai+n-1 + Bi+n-1) A = Cripple, i+n-1 (the carry output for the ripple adder summing bits i to i+n-1) B = Cout, i-1.
This greatly reduces …show more content…
In this case, the RCA is as slow as it is large. Actually, RCA are fast only for some configurations of the input words, where carry signals are generated at some positions. Depending on the position at which a carry signal has been generated, the propagation time can be variable. Carry Skip Adders take advantage both of the generation or the propagation of the carry signal. They are divided into blocks, where a special circuit detects quickly if all the bits to be added are different (Pi = 1 in the entire block). The signal produced by this circuit will be called block propagation signal. If the carry is propagated at all positions in the block, then the carry signal entering into the block can directly bypass it and so be transmitted through a multiplexer to the next block. As soon as the carry signal is transmitted to a block, it starts to propagate through the block, as if it had been generated at the beginning of the block. Figure 5 shows the structure of a 16-bits skip carry adder, divided into 2, 4 and 8-blocks. It becomes now obvious that there exist a trade-off between the speed …show more content…
ak+1 ak+2 ak 010101 al+2 al+1 al …….
….. bk+1 bk+2 bk 101010 bl+2 bl+1 bl …….
If Cl+3 = 1 then carry will propagate to position k; to speed-up operation, propagation is skipped to position i without waiting for rippling operation time varies according to operands as in carry-complete addition to implement carry-skip adder, stages are divided into blocks and carry-skip logic is added to each block to detect when carry-in the block can be passed directly to the next block define carry transfer Ti = ai + bi carry skipping can be detected for a block size of m as follows (carry propagates through all stages): Tj . Tj+1…….Tj+m-1 = 1 ( = (aj + bj) . (aj+1 + bj+1) …. ) note: this takes into account both propagated and generated carries!
Carry out from the block (m-bits in a block) is Tj . Tj+1 …. Tj+m-1 . Cj + Cj+m Skipped