Abstract: In one embodiment of a header-compression method, a timestamp value is divided by a stride value using a plurality of binary-shift operations corresponding to a Taylor expansion series of the reciprocal stride value in a base of ½. When the division-logic circuitry of an arithmetic logic unit in the corresponding communication device is not designed to handle operands that can accommodate the length of the timestamp and/or stride values, the header-compression method can advantageously be used to improve the speed and efficiency of timestamp compression in communication devices.

Abstract: An optimized floating point multiplier rounding circuit that minimizes the increase of the critical timing path of the calculation. The values of the temporary mantissa required to make the rounding decision are calculated simultaneously by the circuit shown in the invention.

Abstract: A Montgomery inverse calculation device includes a plurality of registers each storing a value of a variable, a modulus register storing a modulus, a multiplier performing multiplication on the modulus. A comparator compares the value of the variable stored in each of the registers with an output value of the multiplier and generates a plurality of control signals. A plurality of shifters shifts bits of a value of a variable stored in a corresponding register among the registers in response to at least one first control signal, and a quotient generation block calculates a quotient of mod 2m with respect to values output from some of the shifters in response to a second control signal. A calculation block calculates an updated value of an output value of each of the shifters using the quotient in response to at least one third control signal.

Abstract: A method for accelerating a pseudo-random input bit flow (PRBS(T1)), generated at a first relatively low dock frequency (f1), into an identical output bit flow (PRBS(T0)) at a second relatively high dock frequency (f0), comprising: collecting the output bit flow, delaying the collected flow by a predetermined value (?); and combining the delayed flow with the input bit flow.

Abstract: In order to reduce the area and power consumption of MAC units, some aspects of the present disclosure relate to MAC units having a feedback path with an arithmetic element disposed thereon. The arithmetic element is often controlled so as to limit the number of bits needed in the data path, thereby limiting power and area required for the MAC unit.

Abstract: A method, apparatus and program storage device that provides a shift process with saturation for digital signal processor operations are disclosed. An instruction is generated for shifting an operand to either maximum or the minimum value depending on the bit of data input when saturation occurs. A saturation detection circuit is combined with an arithmetic shifter and a final decision multiplexor. The final decision multiplexor receives the output from the arithmetic shifter and the saturated value from the saturation circuit. When saturation is detected by the saturation detection circuit, the final decision multiplexor selects the saturate minimum or the saturate maximum depending on whether the MSB of the data in equals one or zero, respectively.

Abstract: A divider circuit includes: a register which is configured of an even number of bits and in which a dividend data is stored. A shift operation section is configured to acquire a data stored in an upper bit portion of the register when the even number of bits of the register is equally divided to the upper bit portion and a lower bit portion, as a quotient data when the dividend data is divided by a maximum of a divisor data which can be expressed by a half of the even number of bits of the register.

Abstract: An apparatus having a carryless preformat unit, a Booth encoder, a compressor, a left shifter, and exclusive-OR logic. The carryless preformat unit receives a multiplier operand and partitions the multiplier operand into parts. The Booth encoder receives the parts and directs selection of first partial products of a multiplicand that do not reflect implicit carry operations. The compressor sums the first partial products via a configuration of carry save adders that generate sum bits and carry bits, where generation of the carry bits is disabled during execution of the carryless multiplication. The left shifter shifts bits of one or more outputs of the compressor. The exclusive-OR logic is coupled to the compressor and the left shifter, and is configured to execute an exclusive-OR function on the outputs to yield a carryless multiplication result.

Abstract: An apparatus having operand registers, an opcode dectector, a carryless preformat unit, a compressor, a left shifter, and exclusive-OR logic. The operand registers receive operands for a carryless multiplication. The opcode dectector receives a carryless multiplication instruction, and asserts a carryless signal. The carryless preformat unit partitions a first operand into a plurality of parts that are such that a Booth encoder is precluded from selection of second partial products of a second operand, where the second partial products reflect implicit carry operations. The compressor sums first partial products of the second operand via carry save adders arranged in a Wallace tree configuration, where generation of carry bits is disabled. The left shifter shifts one or more outputs of the compressor. The exclusive-OR logic executes an exclusive-OR function to yield a carryless multiplication result.

Abstract: A fixed multiply-add (FMA) apparatus and method are provided. The FMA apparatus includes a partial product generator configured to generate a partial sum and a partial carry, a carry save adder configured to generate a partial sum having a first bit size and a partial carry having the first bit size by adding the partial sum and the partial carry to least significant bits (LSBs) of the mantissa of a third floating-point number, a carry select adder configured to generate a mantissa having a second bit size by adding the first bit-size partial sum and the first bit-size partial carry to most significant bits (MSBs) of the third floating-point number, and a selector configured to transmit the first bit-size partial sum and the first bit-size partial carry to the carry save adder or the carry select adder according to whether the mantissa of the third floating-point number is zero.

Abstract: Disclosed is a method for generating a sequence and an apparatus for the same which can satisfy the number M? of sequences sufficiently larger than a length N of a sequence required in a wireless communication system. When the generation of a sequence of the wireless communication system is intended, a first sequence is generated from an mth order primitive polynomial determined according to the length of a required sequence. Then, a second sequence and a third sequence are generated from the first sequence, and a remainder and a quotient is obtained by dividing a particular reference parameter by a number equal to or smaller than 2m+1. Next, a fourth sequence having a desired length N is generated by using the io remainder and the quotient. Therefore, it is possible to generate sequences satisfying that the number M? of sequences is sufficiently larger than a length N of the sequence.

Abstract: The present invention provides a low-latency arc-tangent calculation structure and a calculation method thereof. The arc-tangent calculation structure comprises two lookup tables, a subtractor, a sign comparator, a numerical comparator and a shift encoder. The present invention divides the coordinate system into a plurality of sectors for simplifying the lookup tables. The first lookup table is used to perform logarithmic transformation so as to replace a divider with a subtractor. The second lookup table integrates an exponentiation table and an angle table to translate the output of the subtractor into arc-tangent value ?. Then, ? is shifted to a correct angle according to the output of the shift encoder.

Abstract: The present invention provides for calculating a shift amount as a function of a plurality of numbers. At least one decoder and the at least one adder are coupled in parallel. A shifter is configured to compute a value in a plurality of shift stages, and wherein a bit group of the shift amount is employable to affect at least one of the plurality of shift stages, thereby decreasing processing time.

Abstract: An electronic device includes N inputs to receive R input data, R being able to take values from 1 to N, and N outputs. A configurable shift circuit is coupled between the N inputs and N outputs and has a cascade of shift stages, each shift stage comprising at least N controllable multiplexers. Each multiplexer includes first and second elementary inputs respectively coupled to a first input and a second input taken from among the N inputs so as to, on command, not shift a data item present on the first elementary input and shift a data item present on the second elementary input by an elementary shift value dependent on a rank of the shift stage, a direction of the shift being identical for each multiplexer. Control circuitry controls the multiplexers to deliver the R input data on R outputs.

Abstract: A binary rotator which includes an array of n cascaded 2-input multiplexer banks and received at an input 2n-bit binary data words can be used not only for rotation but also for selective reversal, without the necessity of the addition of a further multiplex bank dedicated to the reversal. This is achieved by making groups of multiplexers of at least all but one of the n banks of multiplexers separately controllable by words from control logic, rather than feeding the multiplexer banks with single control bits. The control bits are appropriately selected to provide the desired rotation-cum-reversal with just the 2n×n array of multiplexers, and can themselves be generated by appropriate logic gates.

Abstract: A system for processing sample sequences, that may include an input, a sequence of coupled registers, including an accumulator register, and first circuitry that may be coupled to the accumulator register and to the input. The input may be configured to receive a first number of sample sequences having two or more samples. To process the first number of sample sequences, the first circuitry may be configured to generate a current effective sample corresponding to the sample for each sample in each sample sequence, write the current effective sample to the accumulator register, and shift the contents of each register into a successive register in the sequence of registers. After processing, each register of at least a subset of the sequence of registers may hold a respective final effective sample that may correspond to a different position in a processed sample sequence.

Abstract: A processor includes a shift device for extending the width of a rotator without increasing propagation delays. An extended-width result is obtained by combining a rotation result with a shift result in accordance with a mask that is selected in response to at least a portion of the value of the degree to which a data word is to be shifted.

Abstract: An arithmetic logic and shifting device is disclosed and includes an arithmetic logic unit that has a first input to receive a first operand from a first register port, a second input to receive a second operand from a second register port, and an output to selectively provide a memory address to a memory unit in a first mode of operation and to selectively provide an arithmetic output in a second mode of operation. Further, the arithmetic logic and shifting device includes a programmable shifter device that has a first input to receive data from the memory unit, a second input to receive the arithmetic output, a third input to receive an operation code of a computer execution instruction, and a shifted output to provide shifted data.

Abstract: A decimal multiplication mechanism for fixed and floating point computation in a computer having a coefficient mechanism without resulting leading zero detection (LZD) and process which assumes that the final product will be M+N digits in length and performs all calculations based on this assumption. Least significant digits that would be truncated are no longer stored, but retained as sticky information which is used to finalize the result product. Once the computation of the product is complete, a final check based on the examination of key bits observed during partial product accumulation is used to determine if the final product is truly M+N digits in length, or M+N?1 digits. If the latter is true, then corrective final product shifting is employed to obtain the proper result. This eliminates the need for dedicated leading zero detection hardware used to determine the number of significant digits in the final product.

Abstract: A method for efficient state transition matrix based LFSR computations are disclosed. A polynomial associated with a linear feedback shift register is defined. This polynomial is used to generate a single step state transition matrix. The single step state transition matrix is then modified into a more general k-step state transition matrix. The resultant combined matrix is reduced in size and can be multiplied by a state input vector, ultimately producing a plurality of next state-input vectors thereby providing improved efficiency in computing a LFSR.

Abstract: Techniques are disclosed for calculating large precision common logarithms. A common logarithm may be calculated using addition and/or subtraction of known logarithm values. Embodiments of the invention permit calculation of common logarithms of real numbers stored within character arrays, where each element of the array corresponds to a digit in the real number.

Abstract: A method of providing wiring efficiency in a permute unit. Multiple selectors receive input data and shared control signals from multiple register files. The permute unit includes multiple multiplexors (MUXs) coupled to multiple logical AND gates. The multiple logical AND gates are coupled to multiple logical OR gates. The logical AND gates are physically separated from the logical OR gates. The logical AND gates receive input from one or more output data signals from the selectors. The logical OR gates combine the one or more output signals from the logical AND gates and provide output data from the permute unit.

Abstract: A shift register has shift register units. The nth shift register unit includes first to third level control units and first and second driving units. The first and second level control units respectively provide a first clock signal and a first voltage to an output terminal. The first driving unit and the first level control unit are coupled to a first node, and a voltage on the first node is a first control signal. The first driving unit turns on and off the first level control unit in response to an input signal and second and third control signals. The second driving unit turns on and off the second level control unit in response to the first control signal. The third level control unit provides the first voltage to the output terminal in response to a front edge of the first control signal of the (n+2)th shift register unit.

Abstract: An FFT algorithm that splits a large bit width waveform into two parts, making it possible to conduct the FFT with much lower logic resource consumption is disclosed. The waveform is split into its most significant bits and its least significant bits through division in the form of a bit shift. Each partial signal is then put through an FFT algorithm. The MSB FFT output is then right bit shifted. The two partial FFT's are summed to create a single output that is largely equivalent to an FFT of the original waveform. Rounding distortion is reduced by overlapping the MSB and LSB partial signals.

Abstract: In general, in one aspect, the disclosure describes a multiplier that includes a set of multiple multipliers configured in parallel where the set of multiple multipliers have access to a first operand and a second operand to multiply, the first operand having multiple segments and the second operand having multiple segments. The multiplier also includes logic to repeatedly supply a single segment of the second operand to each multiplier of the set of multiple multipliers and to supply multiple respective segments of the first operand to the respective ones of the set of multiple multipliers until each segment of the second operand has been supplied with each segment of the first operand. The logic shifts the output of different ones of the set of multiple multipliers based, at least in part, on the position of the respective segments within the first operand. The multiplier also includes an accumulator coupled to the logic.

Abstract: A QRD processor for computing input signals in a receiver for wireless communication relies upon a combination of multi-dimensional Givens Rotations, Householder Reflections and conventional two-dimensional (2D) Givens Rotations, for computing the QRD of matrices. The proposed technique integrates the benefits of multi-dimensional annihilation capability of Householder reflections plus the low-complexity nature of the conventional 2D Givens rotations. Such integration increases throughput and reduces the hardware complexity, by first decreasing the number of rotation operations required and then by enabling their parallel execution. A pipelined architecture is presented (290) that uses un-rolled pipelined CORDIC processors (245a to 245d) iteratively to improve throughput and resource utilization, while reducing the gate count.

Abstract: A technique for interpolating a series of samples includes constructing a mathematical model of the series that describes its large signal behavior. The model is subtracted from the original series to yield a residue. A discrete Fourier transform (DFT) is taken of the residue, and the DFT is zero-padded. An inverse DFT of the padded result yields an interpolated residue, which is then added back to the mathematical model to construct an interpolated version of the series of samples. Using this technique, accurate interpolation can generally be attained even when the series of samples is not coherently sampled.

Abstract: In one embodiment, a rotator, a mask generator, and circuitry configured to mask the rotated operand output by the rotator with the output mask generated by the mask generator perform a shift operation. The rotator is configured to rotate the input operand by the shift count. The mask generator is configured to generate an output mask by decoding a most significant bit (MSB) field of the shift count to generate a first mask, decoding a least significant bit (LSB) field of the shift count to generate a second mask, logically ANDing the bits of the second mask with the corresponding bit of the first mask and logically ORing the result with an adjacent bit of the first mask that is selected responsive to the shift direction.

Abstract: A method and system to compensate for inaccuracy associated with processing values with finite precision includes a process for selecting a display value whereby an initial value is provided in a first numbering system. The initial value is then converted into an equivalent stored value in a second numbering system. Then a display value in the first numbering system is determined and selected such that the selected display value includes the least number of significant digits that convert from the first numbering system to the second numbering system exactly as the stored value. The selected display value in the first numbering system is then used for display and/or further processing when the stored value in the second numbering system is recalled.

Abstract: A fused multiply add (FMA) unit includes an alignment counter configured to calculate an alignment shift count, an aligner configured to align an addend input based on the alignment shift count and output an aligned addend, a multiplier configured to multiply a first multiplicand input and a second multiplicand input and output a product, an adder configured to add the aligned addend and the product and output a sum without determining the sign of the sum or complementing the sum, a normalizer configured to receive the sum directly from the adder and normalize the sum irrespective of the sign of the sum and output a normalized sum, and a rounder configured to round and complement-adjust the normalized sum and output a final mantissa.

Abstract: Some embodiments present a method of performing a variable shift operation. This method can be used by a microprocessor that does not allow variable shift operation for certain operand sizes. The method simulates a shift instruction that shifts an operand by a shift count. The method identifies a first shift command and a second shift command. The method computes a mask value. The mask value depends on whether the shift count is less than half of the operand size or greater than or equal to half of the operand size. The method uses the mask value to cause one of the first shift command and the second shift command to produce no shift. In some embodiments, the method allows for the shift count to be specified in bytes or in bits.

Abstract: A CORDIC engine includes an N-stage CORDIC processor for performing N micro-iterations of a CORDIC algorithm and generating a 3-vector CORDIC output responsive to a 3-vector CORDIC input. A counter counts a number of M macro-iterations for the CORDIC algorithm and indicates a start of the cycle iterations. A multiplexer selects an input to the N-stage CORDIC processor as the 3-vector CORDIC input at the start of the cycle iterations or the 3-vector CORDIC output at other times. The CORDIC algorithm is complete after N*M clock cycles by generating N micro-iterations for each of the M macro-iterations. In some embodiments, the CORDIC engine is coupled to programmable logic blocks as part of a programmable logic array.

Abstract: Circuitry performing Discrete Fourier Transforms. The circuitry can be provided in a fixed logic device, or can be configured into a programmable integrated circuit device such as a programmable logic device. The circuitry includes a floating-point addition stage for adding mantissas of input values of the Discrete Fourier Transform operation, and a fixed-point stage for multiplying outputs of the floating-point addition stage by twiddle factors. The fixed-point stage includes memory for storing a plurality of sets of twiddle factors, each of those sets including copies of a respective twiddle factor shifted by different amounts, and circuitry for determining a difference between exponents of the outputs of the floating-point stage, and for using that difference as an index to select from among those copies of that respective twiddle factor in each of the sets.

Abstract: A decimal floating point finite number in a decimal floating point format is composed from the number in a different format. A decimal floating point format includes fields to hold information relating to the sign, exponent and significand of the decimal floating point finite number. Other decimal floating point data, including infinities and NaNs (not a number), are also composed. Decimal floating point data are also decomposed from the decimal floating point format to a different format. For composition and decomposition, one or more instructions may be employed, including a shift significand instruction.

Abstract: Apparatus and methods are disclosed for a floating point adder having half-adder capability that does not have the overhead of determining half-adder conditions prior to starting the SED, LED, and EXP datapaths.

Abstract: A plurality of specialized processing blocks in a programmable logic device, including multipliers and circuitry for adding results of those multipliers, can be configured as a larger multiplier by adding to the specialized processing blocks selectable circuitry for shifting multiplier results before adding. In one embodiment, this allows all but the final addition to take place in specialized processing blocks, with the final addition occurring in programmable logic. In another embodiment, additional compression and adding circuitry allows even the final addition to occur in the specialized processing blocks.

Abstract: A method for a Galois Field multiply includes executing first and second instructions. The first instruction includes receiving a first input, such as a first variable, receiving a second input, such as a second variable, performing a polynomial multiplication over GF(2m), using the first and second inputs, and producing a product. The second instruction includes receiving a third input, which may be the product from the first instruction, receiving a fourth input, which is a predetermined generator polynomial to operate upon the product, receiving a fifth input, which is a length of the predetermined generator polynomial, to limit operation of the predetermined generator polynomial upon the product, and computing, via the predetermined generator polynomial limited by the length, a modulus of the product with respect to a divisor. A hardware block is also described.

Abstract: Method and apparatus for performing a shift and XOR operation. In one embodiment, an apparatus includes execution resources to execute a first instruction. In response to the first instruction, said execution resources perform a shift and XOR on at least one value.

Abstract: Some embodiments provide a method of presenting virtual memory as narrower and deeper than a physical memory. The method receives a memory address location including a set of real memory address bits and a set of virtual memory position bits. The method retrieves an original memory word from a physical memory using the real memory address bits. The method shifts the original memory word by an amount determined by the virtual memory position bits by using a barrel shifter, creating a shifted memory word. The method reads a part of the shifted memory word.

Abstract: In one embodiment, a forward substitution component performs forward substitution based on a lower-triangular matrix and an input vector to generate an output vector. The forward substitution component has memory, a first permuter, an XOR gate array, and a second permuter. The memory stores output sub-vectors of the output vector. The first permuter permutates one or more previously generated output sub-vectors stored in the memory based on one or more permutation coefficients corresponding to a current block row of the lower-triangular matrix to generate one or more permuted sub-vectors. The XOR gate array performs exclusive disjunction on (i) the one or more permuted sub-vectors and (ii) a current input sub-vector of the input vector to generate an intermediate sub-vector. The second permuter permutates the intermediate sub-vector based on a permutation coefficient corresponding to another block in the current block row to generate a current output sub-vector of the output vector.

Abstract: In one embodiment, a matrix-vector multiplication (MVM) component generates a product vector based on (i) an input matrix and (ii) an input vector. The MVM component has a permuter, memory, and an XOR gate array. The permuter permutates, for each input sub-vector of the input vector, the input sub-vector based on a set of permutation coefficients to generate a set of permuted input sub-vectors. The memory stores a set of intermediate product sub-vectors corresponding to the product vector. The XOR gate array performs, for each input sub-vector, exclusive disjunction on (i) the set of permuted input sub-vectors and (ii) the set of intermediate product sub-vectors to update the set of intermediate product subvectors, such that all of the intermediate product sub-vectors in the set are updated based on a current input sub-vector before updating any of the intermediate product sub-vectors in the set based on a subsequent input sub-vector.

Abstract: A floating point divider includes a mantissa repetitive processing unit and an operation execution control unit. The mantissa repetitive processing unit calculates a quotient and a partial remainder by a digit-recurrence process for a mantissa of a dividend of an input operand. The operation execution control unit determines a bit value at a specified position uniquely specified based on a radix of an operation execution process with respect to the partial remainder. The mantissa repetitive processing unit reduces the number of digit-recurrence processes by calculating a quotient and a remainder based on a determining result of the operation execution control unit. The number of bits of the quotient is double of that of a quotient calculated once every the digit-recurrence process. The number of left-shift processes processed on the remainder is double of that of a remainder calculated once every the digit-recurrence process.

Abstract: A method and system to perform shifting and rounding operations within a microprocessor, such as, for example, a digital signal processor, during execution of a single instruction are described. An instruction to shift and round data within a source register unit of a register file structure is received within a processing unit. The instruction includes a shifting bit value indicating the bit amount for a right shift operation and is subsequently executed to shift data within the source register unit to the right by an encoded bit value, calculated by subtracting a single bit from the shifting bit value contained within the instruction. A predetermined bit extension is further inserted within the vacated bit positions adjacent to the shifted data. Subsequently, an addition operation is performed on the shifted data and a unitary integer value is added to the shifted data to obtain resulting data.

Abstract: A operator is located between two converters that convert data between floating-point format and a predetermined format. The operator operates on predetermined format data, which consists of the same sign bit, the same exponent, and the two's complement of the mantissa of the corresponding floating-point data. When the operator is an arithmetic logic unit (ALU), the number of operations for a given calculation can be reduced.

Abstract: A bit field operation circuit has a first shift unit, a mask shift amount control circuit, a second shift unit, a logic operation unit, and a selection unit. The first shift unit outputs a first intermediate data based on a first control signal. The mask shift amount control circuit outputs a mask shift control signal in accordance with a mask shift amount. The second shift unit outputs a second intermediate data based on a mask shift control signal. The third shift unit outputs a third intermediate data based on the first control signal. The logic operation unit performs logical operation of the second intermediate data and the third intermediate data, and outputs a mask selection data. The selection unit selects either one of the first intermediate data or the second input data based on the mask selection data to output as output data.

Abstract: A floating point multiplier includes a data path in which a plurality of partial products are calculated and then reduced to a first partial product and a second partial product. Shift amount determining circuitry 100 analyses the exponents of the input operands A and B as well as counting the leading zeros in the fractional portions of these operands to determine an amount of left shift or right shift to be applied by shifting circuitry 200, 202 within the multiplier data path. This shift amount is applied so as to align the partial products so that when they are added they will produce the result C without requiring this to be further shifted. Furthermore, shifting the partial products to the correct alignment in this way in advance of adding these partial products permits injection rounding combined with the adding of the partial products to be employed for cases including subnormal values.

Abstract: Systems and methods for performing multiplication of fixed-point fractional values with the same throughput as addition and subtraction operations, and without loss of accuracy in the result. In one embodiment, a method includes reading data from a pair of source registers that contains multiple single-width multiplicand values. Each multiplicand value in one of the source registers is paired with a corresponding multiplicand value in the other source register. For each pair of multiplicands, a double-width product is generated, then a single-width portion of the product is selected and stored in a target register. The selection of the single-width portion is performed by shifting the double-width products in funnel shifters. The immediate shifting of the double-width products to select the single-width portions allows the operation to achieve the same throughput as addition and subtraction operations.

Abstract: The present invention provides a solution to the shortcomings of the traditional two's complement system that is commonly utilized in modern computing systems and digital signal processors for calculating harmonic analysis using a discrete time-frequency transform. In the negative two's complement processor a n-bit number, A, has a sign bit, an?1, and n?1 fractional bits, an?2, an?3, . . . , a0. The value of an n-bit fractional negative two's complement number is: A = a n - 1 + ? i = 0 n - 2 ? - a i ? 2 i - n + 1 .

Abstract: A discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) circuit includes a microcode memory, a processor, and a butterfly operation circuit. The microcode memory stores multiple microcode groups corresponding to DCT/IDCT operations and each of the microcode groups includes a series of microcodes. The processor obtains one of the microcode groups corresponding to one of the DCT/IDCT operations to be performed and retrieves microcodes in the obtained microcode group in sequence. The butterfly operation circuit performs butterfly operations according to the retrieved microcodes to execute one of the DCT/IDCT operations.

Abstract: Method, apparatus, and program means for performing bitstream buffer manipulation with a SIMD merge instruction. The method of one embodiment comprises determining whether any unprocessed data bits for a partial variable length symbol exist in a first data block is made. A shift merge operation is performed to merge the unprocessed data bits from the first data block with a second data block. A merged data block is formed. A merged variable length symbol comprised of the unprocessed data bits and a plurality of data bits from the second data block is extracted from the merged data block.