Performing division is a difficult task as we have seen in case of fixed point arithmetic also. Divider architectures are complex to implement. Floating point division is nothing but a fixed point division with some extra hardwares to take care for the exponents. This extra hardwares make the divider circuit more complex. A floating point […]
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Floating point multiplication is comparatively easy than the floating point addition algorithm but off course consumes more hardware than fixed point multiplier circuit. Major hardware block is the multiplier which is same as fixed point multiplier. This multiplier is used to multiply the mantissas of the two numbers. A floating point multiplication between two numbers
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Compared to a fixed point addition and subtraction, a floating point addition and subtraction is more complex and hardware consuming. This is because exponent field is not present in case of fixed point arithmetic. A floating point addition of two numbers and can be expressed as Here, it is considered that . In this case,
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Generally the FPGA based architectures or ASIC based implementations are fixed point arithmetic based. But the majority of dedicated controllers are floating point based. It may require to interface a FPGA to a micro controller and then a fixed point to floating point conversion unit will be required. In order to discuss the floating point
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In a binary number, leading zeros are the zero digits in the most significant positions of data, up to the position in which the first one is present. For a binary number the leading leading zero count is 4. Leading zero counter is a very important combinational circuit in designing the floating-point architectures to do
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Interfacing ADC with FPGA board is important when we need to acquire an analog signal to process it in FPGA. In many academic projects we are asked to demonstrate the real time application of a digital system implemented on FPGA. In doing that, we find it difficult to interface an ADC chip with FPGA as
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A video controller generates the synchronization signals and outputs data pixels serially through the VGA port of the FPGA board. The synchronization signals generator circuit (vga_sync) generates the timing and control signals. The hsync and vsync signals control the horizontal and vertical scans. The pixel_x and pixel_y signals specify the current location of the pixel.
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The fast multiplication can be achieved in three general ways. The sequential multipliers sequentially generates the partial products and adds them with the previously stored partial products. In the second method, high speed parallel multipliers generate the partial products in parallel and adds them by a fast multi-operand adder. The third method corresponds to use
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In the previous tutorials, we have discussed techniques which can be used to achieve fast multiplication. But when the multiplicand and the multiplier are same, there must be some way to simplify the implementation. Thus squaring operation does not require the full length hardware of a multiplier. In applications where a squaring operation is required,
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Chris Wallace in 1964 gave some suggestions on fast multiplication. In order to achieve high speed without consuming extra hardware he suggested techniques. He proposes to use the basic HAs and FAs as basic elements for operand reduction. He applied operand reduction in parallel layers and achieve better speed. The steps are Obtain the partial products
Wallace and Dedda Multiplier Design Read More »
Booth’s algorithm is a powerful technique to achieve fast multiplication. Booth’s algorithm can be employed either sequentially or with the help of fast addition methods or in the form of array multiplication. In this tutorial, Booth’s Radix-4 algorithm is used to form an architecture to multiply two 6-bit numbers in the form of array multiplier.
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Several techniques are suggested for partial products accumulation. Some of them targets to reduce the logic elements to reduce hardware complexity whereas some of them targets to reduce numbers of levels in the tree of partial products to achieve high speed. As the number of levels increases irregularity in the design also increases. The irregularities
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Earlier we have discussed how the partial products for a unsigned multiplier can be accumulated using suitable organization and consuming minimum number of counters. In this section, accumulation will be done by considering negative partial products. If some of the partial products are negative numbers represented in two’s complement number system, then matrix of bits
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A basic circuit to accumulate two single bits is a half-adder (HA) and a full-adder (FA) accumulates three bits. Thus a HA is called as 2:2 counter and a FA is called a 3:2 counter. Again an HA is hardware efficient than a FA. Carry save adders (CSA) operates on multiple operands. A basic CSA
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Like Booth’s multiplication algorithm another method reduction of partial products is implementing higher multipliers by smaller ones. The larger multiplier blocks can be realized using smaller multiplier blocks. A multiplier can be realized using four multiplier blocks. This is based on the following equation where is the most significant halve of A, is the most
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