Sequential Multiplier is an old method to multiply two binary numbers. But it is also relevant in many architectures and it is the base of many newly developed multiplication techniques. The multiplication between a and b is shown below. The multiplication between two operands a and b can be considered as add the operand a […]
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Array multiplier is very popular for multiplication of binary numbers. Array multiplier resembles the pen and paper method of multiplication process. Array multiplication process for two 4-bit unsigned numbers a and b is shown below. On the contrary to the sequential multiplier, array multiplier is parallel. A array of full adders are used for the
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Our objective is to divide A by B where both A and B can be positive or negative. The division operation can be expressed as by the following equation by considering 4 bit data width. where Q is the quotient and R is the remainder. The division operation is carried out by subsequent stages where
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Newton-Raphson’s iterative algorithm is a very popular method to approximate a given function. It can be used to compute reciprocal of a given number. The Newton-Raphson’s iterative equation is where is the first derivative of . The function which is used to compute the reciprocal of a number is , where D is the input
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Division operation is the most complex operation to perform among all the arithmetic operations and it is also time consuming. The equation of a division operation is where N is the dividend, D is the divisor, Q is the Quotient and R is the remainder. The remainder R is less than D. In implementation of
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The division operation is carried away by assuming fractional numbers. The Non-Restoring division algorithm is shown below. Initially R is set equal to N and n is the data width. The operands are in two’s compliment form where MSB bit is the signed bit. In Non-Restoring divider, quotient take the digit set {-1,1}. At the
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The division operation is carried away by assuming fractional numbers and it is assumed that D and N are positive numbers. The Restoring division algorithm is shown below. Here n is the data width and R is set to N initially. An example of Restoring division is given below. Here N = 0.5 (0.100) and
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COordinate Rotation Digital Computer (CORDIC) is a simple and efficient algorithm to compute arithmetic, trigonometric and hyperbolic functions. In many fields such as DSP, image processing, communication or in industrial sectors, researchers are using CORDIC algorithm to optimize design performance. CORDIC was conceived in 1956 by Jack E. Volder thus it sometimes called as Volder’s
The Gold-Schmidt division is one of the popular fast division methods. It evaluates the division operation by iterative multiplications. The equations which govern Gold-Schmidt division are The major advantage of Gold-Schmidt division is its low latency. In VLSIimplementation where a designer wants to fasten the design performance then this divider can be used. The block
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Design verification is must in designing any system. Design verification and testing is the most tedious job in implementing any complex system. Several foundries are specialized in doing verification and testing. Each and every step of VLSI design needs verification. If there is a fault in any step, one has to go to the early
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Contents for fast addition are Carry Look Ahead Adder Parallel Prefix Adder trees Carry Skip Adder Carry Increment Adder Carry Select Adders Carry Save Addition BCD Addition Addition and subtraction can be performed using the same logic block in two’s complement binary representation. The controlled adder/subtractor logic block is discussed in the tutorial of combinational
Contents for FSM design are Sequence Detector using Mealy Machine Sequence Detector using Moore Machine Serial Adder Vending Machine FSMs, an important category of sequential circuits, are used frequently in designing digital systems. From the daily used electronic machines to the complex digital systems, FSMs are used everywhere. For example, in a station the vending
Contents for the system architectures are Serial Architectures Parallel Architectures Pipelining Comparison Based on the signal acquisition strategy, area and timing constraints digital system architectures can be of the following types Serial Architectures Parallel Architectures Mixed Architectures Go to the Top Serial Architectures The serial architectures process a data stream serially by taking one data
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Contents for memory design are Controlled Register Read Only Memory (ROM) Random Access Memory (RAM) Dual Port Memory Simple Dual Port Memory In digital system design, the usage of memory elements is unavoidable. In some of the systems, data can be pre-stored in a constant memory. Memory elements can be used as temporary storage of
Contents Flip/flops Shift Registers PN Sequence Generator Counters Loadable Counter Clock Division Clock Division by 3 General Approach for Clock Division Sequential Logic Blocks The output of sequential blocks depends on the present state as well as on past state. Sequential circuits work with a reference which is the clock. A clock signal can be
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