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The VHDL Code for full-adder circuit adds three one-bit binary numbers (A B Cin) and outputs two one-bit binary numbers, a sum (S) and a carry (Cout). Truth Table describes the functionality of full adder. sum(S) output is High when odd number of inputs are High. Cout is High, when two or more inputs are High. VHDL Code for full adder can also be constructed with 2 half adder Port mapping in to full adder.

The adder produce carry propagation delay while performing other arithmetic operations like multiplication and divisions as it uses several additions or subtraction steps. This is a major problem for the adder and hence improving the speed of addition will improve the speed of all other arithmetic operations. Hence reducing the carry propagation delay of adders is of great importance. There are different logic design approaches that have been employed to overcome the carry propagation problem. One widely used approach is to employ a carry look-ahead which solves this problem by calculating the carry signals in advance, based on the input signals. This type of adder circuit is called a carry look-ahead adder.

In ripple carry adders, for each adder block, the two bits that are to be added are available instantly. However, each adder block waits for the carry to arrive from its previous block. So, it is not possible to generate the sum and carry of any block until the input carry is known. The block waits for the block to produce its carry. So there will be a considerable time delay which is carry propagation delay.

Consider the above 4-bit ripple carry adder. The sum is produced by the corresponding full adder as soon as the input signals are applied to it. But the carry input is not available on its final steady-state value until carry is available at its steady-state value. Similarly depends on and on . Therefore, though the carry must propagate to all the stages in order that output and carry settle their final steady-state value.

The propagation time is equal to the propagation delay of each adder block, multiplied by the number of adder blocks in the circuit. For example, if each full adder stage has a propagation delay of 20 nanoseconds, then will reach its final correct value after 60 (20 3) nanoseconds. The situation gets worse, if we extend the number of stages for adding more number of bits.

Carry Look-ahead Adder : A carry look-ahead adder reduces the propagation delay by introducing more complex hardware. In this design, the ripple carry design is suitably transformed such that the carry logic over fixed groups of bits of the adder is reduced to two-level logic. Let us discuss the design in detail.

The complexity arises from the part that generates the carry, not the circuit that adds the bits. Now, for the generation of the carry bit, we need to perform a AND between (n+1) inputs. The complexity of the adder comes down to how we perform this AND operation. If we have AND gates, each with a fan-in (number of inputs accepted) of k, then we can find the AND of all the bits in time. This is represented in asymptotic notation as .

The circuit consists of 4 full adders since we are performing operations on 4-bit numbers. There is a control line K that holds a binary value of either 0 or 1 which determines that the operation is carried out is addition or subtraction.

As shown in the figure, the first full adder has a control line directly as its input(input carry Cin), The input A0 (The least significant bit of A) is directly input in the full adder. The third input is the exor of B0 and K. The two outputs produced are Sum/Difference (S0) and Carry (C0).

From the truth table of the half adder we can see that the SUM (S) output is the result of the Exclusive-OR gate and the Carry-out (Cout) is the result of the AND gate. Then the Boolean expression for a half adder is as follows.

The main difference between the Full Adder and the previous Half Adder is that a full adder has three inputs. The same two single bit data inputs A and B as before plus an additional Carry-in (C-in) input to receive the carry from a previous stage as shown below.

Then the full adder is a logical circuit that performs an addition operation on three binary digits and just like the half adder, it also generates a carry out to the next addition column. Then a Carry-in is a possible carry from a less significant digit, while a Carry-out represents a carry to a more significant digit.

As the full adder circuit above is basically two half adders connected together, the truth table for the full adder includes an additional column to take into account the Carry-in, CIN input as well as the summed output, S and the Carry-out, COUT bit.

The second binary adder in the chain also produces a summed output (the 2nd bit) plus another carry-out bit and we can keep adding more full adders to the combination to add larger numbers, linking the carry bit output from the first full binary adder to the next full adder, and so forth. An example of a 4-bit adder is given below.

When the size of the bits being added is not too large for example, 4 or 8 bits, or the summing speed of the adder is not important, this delay may not be important. However, when the size of the bits is larger for example 32 or 64 bits used in multi-bit adders, or summation is required at a very high clock speed, this delay may become prohibitively large with the addition processes not being completed correctly within one clock cycle.

One solution is to generate the carry-input signals directly from the A and B inputs rather than using the ripple arrangement above. This then produces another type of binary adder circuit called a Carry Look Ahead Binary Adder where the speed of the parallel adder can be greatly improved using carry-look ahead 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.

4-bit full adder circuits with carry look ahead features are available as standard IC packages in the form of the TTL 4-bit binary adder 74LS83 or the 74LS283 and the CMOS 4008 which can add together two 4-bit binary numbers and generate a SUM and a CARRY output as shown.

There are a number of 4-bit full-adder ICs available such as the 74LS283 and CD4008. which will add two 4-bit binary number and provide an additional input carry bit, as well as an output carry bit, so you can cascade them together to produce 8-bit, 12-bit, 16-bit, adders but the carry propagation delay can be a major issue in large n-bit ripple adders.

A half adder is an arithmetic combinational circuit that takes in two binary digits and adds them. The half adder gives out two outputs, the SUM of the operation and the CARRY generated in the operation. Write a VHDL code using structural, behavioural and data flow modelling.

Q no 1 : Draw the 3 bit parallel adder write its equation of Sum output & Carry outputas you have learned 1 bit full adder and fill the truth table for just 4 combinations asgiven below in table & also insert screen shots of simulation.A0A1A2 B0B1B2 SUM OUT CARRY OUT000 111110 001010 011111 111SUM =Co =

(2) 32 identical Full Adders are used to realized 32-bit ripple carry adder as shown in Figure 1. The carry-propagation delay and sum-propagation delay of each full adder is 10 ns and 12 ns respectively. Find the worst-case propagation delay (in ns) of this 32-bit ripple carry adder? 350c69d7ab