Adder

What is Adder?

In the world of computers, an adder may refer to a specific component in the processor that adds two numbers according to the instructions given.

Technically, it refers to the electronic circuit that adds the amplitudes of the input signals.

Understanding Adder

The digital logic circuit in the CPU of a computer that is used for adding two binary numbers is called an adder.

Typically, these form the fundamental component of the Arithmetic Logic Unit or ALU.

This combination of logic circuits adds two binary numbers but does not have any memory circuits.

It performs an operation that is logically given to it by a Boolean expression.

The final result generated by the adder will typically depend on the given input at any given time.

When one’s or two’s complements are used, it may be insignificant to amend an adder into an adder-subtractor, but the basic adder will need more logic if there are other signed number demonstrations.

The circuits in the adder follow a simple working principle. If it is a full adder, it will use two half adder circuits with the power connections connected by a switch to the two inputs.

However, the output is displayed for each logic gate.

Typically, when the switch is ON or +5 volts, it indicates a logic high, and when it is OFF or 0 volts, it indicates a logic low.

What is Adder Used for?

The primary function of this digital logic circuit is also to perform ALU operations, calculate addresses or act as an increment or decrement operator in the processor.

Typically, an adder is used mainly to add numbers in a computer when the processor is given such instructions. However, depending on the type of the adder, it may also be used for several other applications such as:

• A full adder is used for adding n-bits concurrently because it is a part of other bigger circuits such as Ripple Carry Adder
• Full adders may also be used for carryout multiplication due to the dedicated multiplication circuits in them
• These logic circuits are also used for Program Counter or PC point to the subsequent instruction and
• Full adders can also be used for different graphics related activities being a part of the Graphics Processing Unit.

It is also used to perform other related activities such as calculating table indices.

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What Are the Basic Types of Adder?

There are basically two major types of adders, namely the half adder and the full adder. You will also get multi-bit adders with a couple of other variants.

• Half adders – These are usually designed with a fused arithmetic logic circuit and can add binary numbers in two single bits. The output produced by these adders are sum bit and carry bit.
• Full adders – These are however designed by uniting two half adder circuits and are capable of adding three binary numbers of single bits. Ideally, all full adders are very helpful for the ALU systems and their operations.

In addition to the above major variants, you will also find a few other specific types of adders as mentioned hereunder.

Multi-Bit adders:

These circuits are made by using full adders either serially or in parallel and accordingly referred to as follows:

• Serial adder – This is basically a full adder that has three inputs and two outputs of single bits each. The circuits in it perform binary addition for every clock pulse, bit by bit. This is essentially a sequential logic circuit.
• Parallel adder – This adder performs binary additions much faster because a number of full adders are cascaded in its circuit. It is a combinational logic circuit that is used to add two binary numbers larger than one bit in length.

Quantum adders:

The quantum adders are specially designed circuits. These are typically built by using only the Toffoli gate and CNOT quantum logic gates that offer both quantum full adders and quantum half adders.

Since both Toffoli and CNOT are classical logic gates, these circuits can be used for both classical and reversible computation.

And, numbers can also be added due to the low circuit complexity of the Quantum Fourier Transform.

Analog adders:

Finally, there are the analog adders that are just like the binary adders. This effectively combines two input currents by adding them together.

It can be used to add non-binary signals having a base greater than 2 as well in order to calculate a sum within the limitations of the hardware.

The analog adders are known as the summing amplifiers as well and the technique followed is very effective to reduce the number of transistors to be used in the addition circuit.

Which Adder is Best?

You will get the best performance from the parallel prefix adders used in the VLSI or Very large Scale Integrations applications.

However, you will also get a reasonably high performance from the carry look ahead adder if it is used for two 8-bit number addition operations.

On the other hand, if you want to add three or four 8-bit numbers, you will be better off using a carry save adder in which the last stage is built by a ripple carry adder.

Typically, the exclusive adders with unique design that offers low area and delay in order will provide the best performance and will be able to meet the requirements of the current industry.

It is expected that in the future it will be extended even further by simulating and designing the adders with a greater number of bits such as 16 bits, 32 bits and 64 bits.

Advantages of Adder

• It acts as the fundamental building block for single bit addition
• The design of half adders is very simple
• Half adders can be modified into a half subtractor by simply using an inverter gate
• It offers full swing output
• It is fast in operation
• It consumes low power and
• It is robust to offer transistor sizing and supply voltage scaling.

Disadvantages of Adder

• Lower output drive capability when used in a chain construction like in a ripple adder
• Half adders does not consider or use preceding carry for addition and
• Half adders are not fit for cascading for multi-bit addition.

Why Use Adder?

The need for an adder is for its significant role in helping the Arithmetic Logic Unit for adding binary numbers, though the control unit of the CPU decides which particular operation should be performed by the ALU.

Apart from the basic use, a full adder also serves several other useful purposes such as:

• For introducing specific multiplexers in every Bi to enable switching between it and zero which further helps in producing two’s complements
• For adding more logic in front of an adder so that it can perform at a capacity which is much higher than that of an adder and be changed into an ALU
• For several other specific applications such as in several digital circuits that may perform both computing as well as non-computing operations
• For carryout multiplications and for generating memory addresses and creating program counterpoints
• For creating complex circuits that will help in adding several bits at the same time and
• As a crucial part of the GPU or Graphical Processing Unit.

As for the half adders, on the other hand, the need of them is more profound in the following areas:

• To create a complete adder combination
• For proper functioning of the calculators due to their binary properties and
• For effective operation of the digital measuring devices.

What is Parallel Adder?

Parallel adder is basically a stream of multiple full adders that makes binary addition much faster. The number of full adders in it may vary according to the number of bits that are to be added in the binary digits. Therefore, a parallel adder is actually an n-bit adder which is a cascade of n full adders.

This particular circuit is used mainly to find the sum of two n-bit binary numbers that are more than a bit in length with the use of its combination of several logic circuits.

The bits are added simultaneously by the parallel adders for each clock pulse.

There are many different types of parallel adders available such as:

• Carry Look Ahead Adder
• Carry Save Adder
• Carry Select Adder
• Carry Skip Adder
• Carry By-pass Adder
• Carry Increment Adder and
• Ripple Carry Adder.

The different types of adders offer different usage benefits such as:

• The time needed to complete an operation is not dependent on the number of bits because every operation is parallel and simultaneous
• The operations are completed much faster than serial adders and
• It is much cheaper to use.

However, there are a few downsides to it. One of the most significant drawbacks of it is that the inputs received by the adder at the two ports are instantaneous but the carry ports do not get them until the previous adder completes its operations.

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This results in an operational delay which grows even further when more adders are used.

This is also called the carry propagation delay which is related to the traveling of carry bits.

Half Adder Vs Full Adder

• The half adder and full adder are different in their hardware architectures, with the former being simple and the latter being complex
• The half adder can add two binary inputs and give out a carry and a sum but the full adder, on the other hand, can add three binary inputs to generate the same output
• The half adder does not consider the carry from the prior addition and does not add to the next operation but, in comparison, the digital logic of the full adder considers this previous carry to be helpful in the following addition
• The half adders typically have two logic gates such as the EX-OR gate and the AND gate but, in comparison, the full adders have three logic gates such as an OR gate, two EX-OR gates, and three AND gates
• The half adder features two input bits, A and B, but, in comparison in the full adders there is an extra C input bit apart from the A and B input bits
• The carry equations of the half adder are Sum = A + B, and C = A x B but, in comparison, the carry equations of the full adder are Sum = A + B + Cin and C= A x B + Cin (A + B)
• The half adders are easier to design in comparison to the full adders which are needed to create multiplexers and other critical circuits
• The half adders consume much more power in comparison to the full adders
• The output produced by the half adders is lower than the full adder which allows more combinations
• The speed of operation of the half adders is relatively slower in comparison to the full adder
• The half adders do not support voltage scaling but the full adders do due to their robustness
• The half adder will not function like a full adder but the latter can be used in place of the half adder circuit and
• Half adders are usually used in computers, calculators, digital measuring devices and others while the full adders are used in digital processors, multiple bit addition and other applications.

Conclusion

Adders are a very important component of the CPU organization that helps in adding two binary numbers as well as in other ALU operations.

There are different types of adders available but the major ones are half adders and full adders with each having their distinctive features, offering different benefits.