Half adders and full adders in digital principles
- 1. INTRODUCTION An adder is a digital logic circuit in electronics that is extensively used for the addition of numbers. In many computers and other types of processors, adders are even used to calculate addresses and related activities and calculate table indices in the ALU and even utilized in other parts of the processors. These can be built for many numerical representations like excess-3 or binary coded decimal. Adders are basically classified into two types: Half Adder and Full Adder.
- 2. CLASSIFICATION OF ADDERS Adders are broadly classified into two types. They are: • Half Adder • Full Adder • Half Adder Half Adder is a combinational arithmetic circuit that adds two binary numbers and produces sum bit (S) and carry bit (C) as the output. It is used to add 2 single-bit binary numbers. Full Adder It is a combinational arithmetic circuit constructed by combining two Half Adder circuits. It is used to add 3 one-bit binary numbers.
- 3. CLASSIFICATION (PICTORIAL FORM) HALF ADDER FULL ADDER
- 4. HALF ADDER • Half adder adds two binary digits where the input bits are termed as augend and addend. • It produces two outputs one is the sum and the other is carry. • XOR is applied to both the inputs. • AND gate is applied to both inputs to produce carry.
- 5. TRUTH TABLE FOR HALF ADDER • The 2-bit half adder truth table : 0+0 = 1 0+1 = 1 1+0 = 1 1+1 = 10 INPUTS OUTPUTS A B SUM CARRY 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1
- 6. HALF ADDER TRUTH TABLE • The simplest expression uses the exclusive OR function: Sum = AÅB • An equivalent expression in terms of the basic AND, OR and NOT is: Sum = SUM=A|.B+A.B'
- 7. FULL ADDER • Full adder adds 3 one-bit numbers. • One of the three bits can be referred to as operands. • The other is termed as bit carried in. • The produced output is 2-bit output and these can be referred to as output carry and sum.
- 8. TRUTH TABLE FOR FULL ADDER INPUTS OUTPUTS A B C-IN 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 C-OUT S 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1
- 9. FULL ADDER TRUTH TABLE • The output carry is designated as C-OUT and the normal output is represented as S which is ‘SUM’. • With the above full adder truth-table, the implementation of a full adder circuit can be understood easily. The SUM ‘S’ is produced in two steps: 1. By XORing the provided inputs ‘A’ and ‘B’ 2. The result of A XOR B is then XORed with the C-IN
- 10. THE RELATION BETWEEN HALF ADDER AND FULL ADDER • Half adder produces results and full adder uses half adder to produce some other results. • Similarly, the full adder is of two half adders. • The Full-Adder is the actual block that we use to create the arithmetic circuits.
- 11. WHAT IS MULTIPLEXER??? Multiplexer is a device that has multiple inputs and a single line output. The select lines determine which input is connected to output and also to increase the amount of data that can be sent over a network with certain time. It is called as data selector.
- 12. MULTIPLEXER TYPES 1. 2-1 Multiplexer(1 select line) 2. 4-1 Multiplexer(2 select line) 3. 8-1 Multiplexer(3 select line) 4. 16-1 Multiplexer(4 select line)
- 13. 4 TO 1 MULTIPLEXER
- 14. APPLICATIONS OF MULTIPLEXER Communication System: Acommunication system has a great impact by multiplexer. By using a multiplexer, the efficiency can be increased. Computer Memory: Multiplexers are used in computer memory. Reduces copper lines to connect the memory to other parts of the computer.
- 15. Telephone Network: In telephone networks, multiple audio signals are integrated. Transmission from the Computer of a Satellite: Multiplexer is used to transmit the data signals. From satellite to ground By using GSM satellite. APPLICATIONS OF MULTIPLEXER
- 16. WHAT IS DEMULTIPLEXER??? De-multiplexer is also a device with one input and multiple output lines. It is used to send a signal to one of the many devices. The main difference between a multiplexer and a de-multiplexer is that a multiplexer takes two or more signals and encodes them on a wire, whereas a de-multiplexer does reverse to what the multiplexer does.
- 17. TYPES OF DEMULTIPLEXER De-multiplexers are classified into four types : 1-2 demultiplexer (1 select line) 1-4 demultiplexer (2 select lines) 1-8 demultiplexer (3 select lines) 1-16 demultiplexer (4 select lines)
- 19. APPLICATIONS OF DEMULTIPLEXER Communication System : DE multiplexer receives signal outputs from the multiplexer. At the receiver end it converts them back to the original form. Arithmetic Logic Unit (ALU) : The output of the ALU is fed as an input to the DE multiplexer. And the output of the DE multiplexer is connected to a multiple register.
- 20. Seriestoparallel converter : This converter is used to reconstruct parallel data. Serial data is given as an input to the DE multiplexer at a regular interval. Acounter is attached to detect the data signal. APPLICATIONS OF DEMULTIPLEXER
- 21. Encoder and Decoder Encoders and decoders are fundamental components in digital electronics, primarily used for data conversion and signal processing. Both are combinational logic circuits, but they serve opposite functions.
- 22. Feature Encoder Decoder Input Lines 2n n Output Lines n 2n Function Converts inputs to binary code Converts binary code to outputs Complexity Simpler operation More complex operation Typical Use Transmitting data Receiving and processing data Differences