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Simple System Design Techniques
Published in A. Arockia Bazil Raj, FPGA-Based Embedded System Developer's Guide, 2018
This unwanted delay time is called a propagation delay. Also, another problem called overflow occurs when an n-bit adder adds two parallel numbers together whose sum is greater than or equal to 2n. One solution is to generate the carry input signals directly from the A and B inputs rather than using the ripple arrangement; this is another type of binary adder circuit called a carry look-ahead adder (CLAA), where the speed of the parallel adder can be greatly improved using CLA logic. The advantage of carry look-ahead adders is that the length of time a carry look-ahead adder needs in order to produce the correct sum is independent of the number of data bits used in the operation, unlike the cycle time a parallel ripple adder needs to complete the sum, which is a function of the total number of bits in the addend. A 4-bit full adder circuit with CLA features is available in standard IC packages in the form of the TTL 4-bit binary adder 74LS83, as shown in Figure 3.2b, or the 74LS283 and CMOS 4008, which can add together two 4-bit binary numbers and generate a sum and a carry output 21,25.
Computer Arithmetic
Published in Vojin G. Oklobdzija, Digital Design and Fabrication, 2017
Earl E. Swartzlander, Gensuke Goto
The second step in the fast multiplication process is shown for a 6 by 6 Dadda multiplier on Fig. 11.11. An input 6 by 6 matrix of dots (each dot represents a bit product) is shown as matrix 0. “Regular dots” are formed with an AND gate, dots with an over bar are formed with a NAND gate. Columns having more than four dots (or that will grow to more than four dots due to carries) are reduced by the use of half adders (each half adder takes in two dots and outputs one in the same column and one in the next more significant column) and full adders (each full adder takes in three dots from a column and outputs one in the same column and one in the next more significant column) so that no column in matrix 1 will have more than four dots. Half adders are shown by a “crossed” line in the succeeding matrix and full adders are shown by a line in the succeeding matrix. In each case, the rightmost dot of the pair that is connected by a line is in the column from which the inputs were taken in the preceding matrix for the adder. A special half adder (that forms the sum of its two inputs and 1) is shown with a doubly crossed line. In the succeeding steps, reduction to matrix 2, with no more than three dots per column, and finally matrix 3, with no more than two dots per column, is performed. The reduction shown in Fig. 11.11 (which requires four full-adder delays) is followed by a 10-bit carry propagating adder. Traditionally, the carry propagating adder is realized with a carry lookahead adder.
Basics of the central processing unit
Published in Joseph D. Dumas, Computer Architecture, 2016
Of course, as the old truism goes, there is no such thing as a free lunch. The carry lookahead adder provides superior speed, but the trade-off is greatly increased circuit size and complexity. Notice the trend in the carry equations above. The first one, for c1, has two product terms with the largest term containing two literals. The second one has three product terms with the largest containing three literals, and so on. If we were designing a 32-bit adder, the final carry equation would have 33 terms, with 33 literals in the largest term. We would need an OR gate with a fan-in (number of inputs) of 33, plus 32 AND gates (the largest also having a fan-in of 33), just to produce that one carry bit. Similar logic would be needed for all 32 carries, not to mention the 32 AND gates and 32 OR gates required to produce the carry generate and propagate functions. Logic gates with high fan-in are difficult to construct in silicon, and large numbers of gates take up a great deal of chip space and increase power dissipation. It is possible to piece together an AND gate with many inputs by using two-level AND/AND logic (or to build a larger OR gate using two-level OR/OR logic), but this increases propagation delay and does nothing to reduce the size or power dissipation of the circuit. Now imagine using the carry lookahead logic required to build a 64-bit adder. It would be fast but huge.
Energy Efficient and Variability Immune Adder Circuits using Short Gate FinFET INDEP Technique at 10nm technology node
Published in Australian Journal of Electrical and Electronics Engineering, 2023
Umayia Mushtaq, Md Waseem Akram, Dinesh Prasad
Among the many adder topologies, carry look ahead adder (CLA) has become prominent due to reduction in delay of carry propagation by parallel computing stages. Four-bit CLA architecture is of prime importance in the wide adder design due to the reason that 4-bit adders are used as fundamental units. Hence, the need is to optimise the CLA adder which will bring comprehensive performance enhancement in microprocessor design (Balasubramanian and Mastorakis 2018). In our analysis, the design of 4-bit FinFET CLA is carried out at 10 nm technology node, and the comparison is performed with INDEP FinFET CLA adder as shown in Table 5. Various performance parameters like average power dissipation, propagation delay, power delay product and energy delay product are calculated. The power dissipation is reduced by 8.1% in INDEP FinFET CLA adder. There is a slight increase in propagation delay by 0.75%. The PDP and EDP are reduced by 7.5% and 6.80%, respectively, in case of INDEP FinFET CLA adder, hence resulting in energy-efficient design of the CLA FinFET adder as well.
Design of FIR Filter Using Low-Power and High-Speed Carry Select Adder for Low-Power DSP Applications
Published in IETE Journal of Research, 2023
Siliveri Swetha, N. Siva Sankara Reddy
Carry look-ahead adder is one of the speed-efficient adders which eliminates the drawback of Ripple Carry Adder using carry generation and carry propagation logic. Table 1 shows the CLA function table where input carry is propagating to output carry, shown in Equation (1).