Full Adder is a combinational circuit that performs the arithmetic sum of three input bits. It consists of three inputs and two outputs. Three of the input variables can be defined as A, B, Cin and the two output variables can be defined as S, Cout.

The two input variables A and B represents the two significant bits to be added. The third input Cin represents the carry bit. We have to use two digits because the arithmetic sum of the three binary digits needs two digits. The two outputs represents S for sum and Cout for carry.

For designing a full adder circuit, two half adder circuits and an OR gate is required. It is the simplest way to design a full adder circuit. For this two XOR gates, two AND gates, one OR gate is required.

Circuit Diagram for the Full Adder

S=Cin XOR (A XOR B)
Cout=Cin(AB'+A'B)+AB

Truth Table for the Full Adder

ABCinSCout
00000
00110
01010
01101
10010
10101
11001
11111
Half-Subtractor is a combinational circuit that subtracts two bits and produces their differences. It also has an output to specify if a 1 has been borrowed. Suppose the minuend bit is x and the subtrahend bit is y. If we want to perform x-y, we have to check the relative magnitude between x and y.

If x>y, we have three possibilities: 0-0=0, 1-0=1 and 1-1=0. The result is known as difference bit. If x

...THE 4-BIT ADDERSUBTRACTOR
Introduction
To be able to perform arithmetic, you must first be familiar with numbers. Therefore, although we give a few helping examples, this article is not about binary numerals.
The main interactive circuit at the top of this page is an arithmetic circuit capable of performing both addition and subtraction on any two 4-bit binary numbers. The circuit has a Mode switch that allows you to choose between adding (M=0) and subtracting (M=1). To understand why this circuit works, let’s review binary addition and binary subtraction. We use 4-bit numbers in the examples because the main interactive circuit is a 4-bit adder–subtractor.
Binary addition is certainly easier than decimal addition. You just add 0s and 1s. For example to add the numbers five (0101) and six (0110) together, we just add the respective bits:
Decimal numerals | Binary numerals |
6
+5 | 0110
+0101 |
11 | 1011 |
For binary subtraction, we use 2’s complement to keep things simple. For instance, to perform the operation six (0110) minus five (0101), we first obtain the 2’s complement of five and then add it to six:
Step one: Getting the 2’s complement of 5
1. Flip every bit in five to get 1010.
2. Add one to 1010 to get: 1010 + 1 = 1011.
Step two: Adding the 2’s complement of 5 to 6:
1.
Decimal numerals | Binary...

...University of the East
College of Engineering
Electronics and Communications Engineering Department
Experiment 5:
ADDERS
Lugtu ,John Kelly S.
20081107280
Grade
Engr. Oliver G. Daiton
Instructor
EXPERIMENT NO. 5
ADDERS
OBJECTIVES
1. To verify the operations of a half adder and a full adder.
2. To determine the differences between the half adder and full adder.
3. To study the operation of full adder MSI IC.
SKILLS REQUIRED
For the experiment to proceed smoothly, the student must be
1. Familiar with logic gates.
2. Familiar with addition of binary numbers
MATERIALS AND EQUIPMENTS NEEDED
Logic Trainer or breadboard
Logic ICs: 7486, 7408, 7432, 7483
Connecting wires
Long nose pliers
Optional:
Dc power supply
LED’s
PROCEDURES
PART A. HALF ADDER
Step 1. Connect the circuit as shown in figure 1.
Figure 1. Half AdderCircuit
Step 2. Apply the input combinations given table 1 and observe the output. Which LED represents the SUM and which LED represents the CARRY?
Table 1
SW1
SW2
LED1
LED2
0
0
0
1
1
0
1
1
Step 3. Turn off power and disconnect all wires. Remove the ICs.
PART B. FULL ADDERCIRCUIT
Step 1. Connect the...

...Asynchronous circuits keep the assumption that signals are binary, but remove the assumption that time is discrete. This has several possible benefits:
No clock skew - Clock skew is the difference in arrival times of the clock signal at different parts of the circuit. Since asynchronous circuits by definition have no globally distributed clock, there is no need to worry about clock skew. In contrast, synchronous systems often slow down theircircuits to accommodate the skew. As feature sizes decrease, clock skew becomes a much greater concern.
Lower power - Standard synchronous circuits have to toggle clock lines, and possibly pre-charge and discharge signals, in portions of a circuit unused in the current computation. For example, even though a floating point unit on a processor might not be used in a given instruction stream, the unit still must be operated by the clock. Although asynchronous circuits often require more transitions on the computation path than synchronous circuits, they generally have transitions only in areas involved in the current computation.
Note that there are some techniques in synchronous design that addresses this issue as well.
Average-case instead of worst-case performance - Synchronous circuits must wait until all possible computations have completed before latching the results, yielding worst-case performance....

...Functions of CombinationalCircuits
• Adders
A circuit to perform addition of two binary numbers, to produce a sum and carry out, is called a HalfAdder. In multi-bit binary numbers, after adding the two least significant bits, the addition becomes one of adding two operands plus the carry produced by the previous add. The circuit to implement this operation is called a Full-Adder. Acircuit to add two multi-bit binary numbers together in parallel, or at least pseudo-parallel is called a ripple-carry adder. We will examine each of these circuits below.
Half Adder
The half-adder is described by block diagram, truth table and logic equation for Sum and Carry.
Fig. 7.5 Half Adder block diagram
a 0 0 1 1
b 0 1 0 1
Cout 0 0 0 1
Sum 0 1 1 0 Cout = ab a→ b→ H.A. → Sum → Cout
From the minterms in the truth table we get the following Boolean equations for the circuit. Sum = a’b + ab’ or a ⊕ b
Circuit Diagram for half adder which produces a Sum and Cout
p. 1 of 5
Functions of CombinationalCircuits
Full Adder
The full-adder is described by block diagram, truth table and logic equation for Sum and Carry below.
Fig. 7.6
a 0 0 0 0 1 1 1 1
b 0 0 1 1 0 0 1 1
Cin Cout 0 1 0 1 0 1 0...

...
1. Objective:
The main objective of this project is to design and simulate the One-Bit Full-Adder Using VHDL (hardware description language); which helps us to get familiar with the designing, coding and simulation process using VHDL.
2. Discussion
2.1 One-Bit-Full-Adder
One Bit Full Adder is an important/essential component of design for all types of processor including digital processor, Arm processor, micro processer, etc. A one-bit full adder, used in this simulation process is a device that uses three binary inputs A, B, C-in and two binary outputs sum(s) and c-out. The simulation process was achieved using the VHDL (hardware description language). There are several ways to implement a 1 bit full header. This simulation uses the following implementation to achieve the expected specification for sum(s) and c-out.
(1)
. (2)
The design will use the Boolean function from equation 1 and 2 and produces the final truth table that will similar to the following table:-
Where A, B and are input and S (sum) and are output and carry out representation respectively. The summation is symbolically listed below along with the block diagram in figure 2. To meet the specification, the design must use Boolean operation described in the equation 1 and 2. The visual representation for inputs and outputs are represented in block...

...Full adder[edit source | editbeta]
Schematic symbol for a 1-bit full adder with Cin and Cout drawn on sides of block to emphasize their use in a multi-bit adder
A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A,B, and Cin; A and B are the operands, and Cin is a bit carried in from the next less significant stage.[2] The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit wide binary numbers. The circuit produces a two-bit output, output carry and sum typically represented by the signals Cout and S, where . The one-bit full adder's truth table is:
Full-adder logic diagram
Inputs
Outputs
A
B
Cin
Cout
S
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with and .
In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate...

...lab.
A joint lab report may be submitted each week.
Each one of you is responsible for the entire report.
If you have a problem getting in touch with your partner after the lab, then you have to prepare the complete report by yourself.
Make sure that you have your own copy of all the data needed for the lab report. Bring with you to lab a USB memory stick and/or email data to yourself.
The lab reports should be concise and may be handwritten, but typed is preferred.
Remember: Part of the grade is based on neatness and clarity of presentation.
There is no need for excessive prose.
Just explain what you did in the lab, what the results were, what problems you encountered, and their possible reasons.
Show circuit designs and wiring diagrams.
Picture of your circuit can be used.
Present results of the measurements, such as electronic data, and compare them directly to theoretical predictions.
Make two copies of all plots and data files required to be turned in (one for you and one for your partner).
Label all of your plots in your lab reports. Make sure each plot has a meaningful title. Label clearly all axes (with the names of the variables) and give the units, etc. Identify clearly each curve so that your TA can easily understand the origin of all of your data that is displayed in the plots. You will lose points on your lab report for each plot that is not properly annotated.
You may email your lab (and pre-labs) to me...

...Final Project, 4-bit Ripple Carry Adder
1. Introduction
In this project, a 4 -bit ripple carry adder is designed by using dynamic Manchester carry
chain. This adder should be designed in Cadence Virtuoso for both schematics and layout.
This adder has 9 inputs, A0~A3, B0~B3 and CLK. When the design is finished, it should
be checked in HSPICE for the functionality correctness. The worst case delay in this
adder should be found by HSPICE as well.
2. Design
The figure shown below is the schema tics of dynamic carry chain.
Figure 1 Manchester Carry Chain
.
A
B
������������
S
������������
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
Table 1 Full Adder Truth Table
From the truth table of full adder, the functions of P and G are easily to get
P =A ⊕ B
G =AB
The formula below shows the sum bit.
S (G, P) = ( A ⊕ B) ⊕ ������������
S (G, P) = P ⊕ ������������
3. Schematics
From the schematics and formula shows above, an Inverter, AND gate and XOR gate
should be designed to finish the 4 -bit ripple carry adder using Manchester carry chain.
Inverter
An inverter uses one NMOS transistor a nd one PMOS to implement.
The figure below shows schematics of inverter....