Vhdl code for multiplier pdf

We have covered the 2-bit binary multiplier in detail in our digital electronics course. In this article, we will focus more on the VHDL code of the circuit. As we know that in the dataflow modeling style, we describe the flow of data through every gate using equations. After including the library, we need to define an entity in which we define our input and output ports of the circuit.

Then we end the entity using the end keyword. In the above code, architecture is the keyword used to define architecture. Then we specify the name of the entity, for which we are writing the architecture, i.

Now that we have completed the entity-architecture pair, we use the begin keyword after which we start writing the code for the architecture, if we have to define any component or signal, we define it before the keyword begin.

But in P 1 , we have to do a sum of two bits coming from two AND gates, as shown in the figure. Check out the sum output below; it is the EX-OR of the two inputs. Now look at P 2 , it looks confusing at first. But the job is not done yet. P 2 is actually the output of the SUM component of the second half adder. As we saw earlier, the sum component of the half adder is basically the EXORing of its two inputs.

As its name suggests, in this modeling, we define the behavior of the entity using sequential statements. So we will talk only about the architecture here, the architecture of a 2-bit multiplier in behavioral style modeling is shown below. We will start writing the architecture using architecture keyword and a label and then bind it to the entity and use begin keyword to write inside the architecture.

Then we start a process , it contains a set of instructions that will be executed sequentially, and if the program has multiple processes, then all processes will run concurrently. Arguments passed to the process are called its sensitivity list. Like in process A,B , A, B is the sensitivity list, and whenever the value of either A or B changes, the process will be triggered, and all statements inside it will be executed. Here also begin keyword is used to start writing inside the process.

For, eg. Similarly, we cover all values of B for all cases of A. In structural modeling, we describe the circuit by interconnections of individual components of the circuit.

For an output port, instead of using out bit we have used buffer , this is because out bit cannot be read by the circuit that precedes it. We will explain it in detail while explaining the architecture. The rest of the entity is the same. We need some AND gates and Half adders to realize the circuit. So now we define components that will be used in the architecture.

Then we will declare the architecture of the multiplier and define the components using the component keyword in VHDL.

Now, we need to initialize some signals because, as we know that to interconnect components, we have to use signals.

As usual, we start with begin keyword and instantiate the components using component instantiation statements. This is because we had to connect the output of one component to the input of another component instead of the output port. So to carry it, we need a signal which is used for interconnections of components in structural modeling.

It basically injects the provided values into its input ports and reads its output ports and shows as waveforms. However, other scaling factors may be used occasionally.

This position is indicated as the exponent component in the internal representation, and floating point can thus be thought of as a computer realization of scientific notation. The format for single precision floating point number is shown in figure above. In this project we make use of only single precision floating point multiplier because of less complexity.

The exponent is a signed number represented using the bias method with a bias of The term biased exponent refers to the unsigned number contained in bits 1 through 8 and unbiased exponent means the actual power to which 2 is to be raised. The fraction represents a number less than 1, but the significand of the floating-point number is 1 plus the fraction part.

In other words, if e is the biased exponent and f is the value of the fraction field, the number being represented as: 1. To reduce the number of partial products to be added, Modified Booth algorithm [3][4] is one of the most popular algorithms. The simple serial by parallel booth multiplier is particularly well suited for bit serial processors implemented in FPGAs without carry chains because all of its routing is to nearest neighbours with the exception of the input.

The serial input must be sign extended to a length equal to the sum of the lengths of the serial input and parallel input to avoid overflow, which means this multiplier takes more clocks to complete than the scaling accumulator version.

This is the structure used in the venerable TTL serial by parallel multiplier. One operand is fed to the circuit in parallel while the other is serial. N partial products are formed each cycle. Let us take an example: Using Booth algorithm multiply A and B. Similarly, the RM mode can be implemented as the RZ mode for positive numbers and as the RI mode for negative numbers. To perform IEEE rounding [6] using a conventional algorithm, we have to perform the following: Step 1 C and S Computation: Compute C and S to a precision of 2N bits by generating the partial products and reducing them with a partial product reduction network.

Step 4 Rounding Bits Computation: Compute the g and s bits. Based on the rounding mode and rounding bits, add a rounding one unit-in-the-last-place ulp to Rh when necessary.

The lower order N-1 bits are among the bits that the hardware needs to examine for rounding. For notational simplicity, we define the binary point to be at N-1th bit of C and S. Note that Rh in this case is different from Ri and denotes the higher order N bits of R after the normalization step. Several implementation difficulties associated with the IEEE rounding specification can now be identified. First, and need to be computed to a precision of bits, requiring additional hard-ware.

Second, correct rounding in the RN, RP, and RM modes depends on the bit, incurring additional delay because must first be computed and then rounded with an extra addition step. Finally, two normalization steps are potentially needed as rounding may cause the normalized significant of the result to again overflow, requiring a post-round normalization right shift.

Shabiul Islam, Mohd. In this project, pipelined floating point multiplication is divided into three stages. Stage 1 checks whether the operand is 0 and report the result accordingly. Stage 2 determines the product sign, add exponents and multiply fractions. Stage3 normalize and concatenate the product.

The effect of merging different coarse-grained types into larger FPUs is also studied. With advances in technology, many researchers have tried and are trying to design multipliers which offer either of the following design targets — high speed, low power consumption, regularity of layout and hence less area or even combination of them in one multiplier thus making them suitable for various high speed, low power and compact VLSI implementation.

By using serial by parallel Booth multiplier we see that in parallel multipliers number of partial products to be added is the main parameter that determines the performance of the multiplier. To reduce the number of partial products to be added, Modified Booth algorithm is one of the most popular algorithms.