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Questions and Answers
What is the primary function of a full adder?
What is the primary function of a full adder?
How does a BCD adder differ from a binary adder?
How does a BCD adder differ from a binary adder?
What is the role of a half subtractor in digital circuits?
What is the role of a half subtractor in digital circuits?
Which method is primarily used for binary subtraction in logic circuits?
Which method is primarily used for binary subtraction in logic circuits?
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What is the function of a multiplexer in digital circuits?
What is the function of a multiplexer in digital circuits?
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Which of the following statements is true about binary adders?
Which of the following statements is true about binary adders?
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What distinction distinguishes a full subtractor from a half subtractor?
What distinction distinguishes a full subtractor from a half subtractor?
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What describes the function of a comparator in digital circuits?
What describes the function of a comparator in digital circuits?
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What is the primary function of a demultiplexer?
What is the primary function of a demultiplexer?
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How many output lines does an encoder with 4 input lines have?
How many output lines does an encoder with 4 input lines have?
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Which of the following accurately describes a decoder?
Which of the following accurately describes a decoder?
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What characteristic defines a non-weighted code in binary coding?
What characteristic defines a non-weighted code in binary coding?
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What is the primary application of Gray code?
What is the primary application of Gray code?
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What type of data conversion do encoders perform?
What type of data conversion do encoders perform?
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What distinguishes binary code from binary-coded decimal (BCD)?
What distinguishes binary code from binary-coded decimal (BCD)?
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What does the term 'weighted codes' refer to in binary coding?
What does the term 'weighted codes' refer to in binary coding?
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Study Notes
Combinational Logic Circuit
- A combinational logic circuit is a type of circuit whose output at any given time is determined solely by its current input.
- Logic gates and their combinations are the building blocks of combinational logic circuits.
- Examples of combinational logic circuits are adders, subtractors, decoders, encoders, multiplexers, demultiplexers, and comparators.
Error Detector/Parity Generator
- An error detector circuit is designed to detect errors in data transmitted over a communication channel.
- A parity generator is used to add an extra bit (parity bit) to a data word to ensure that the total number of "1" bits in the data word is either even or odd, depending on the parity scheme.
Adder
- An adder circuit is used to perform the addition of binary numbers.
- Different types of adders are designed to carry out addition at varying levels of complexity.
- Adders are essential components in arithmetic logic units (ALUs), processors, and other digital systems.
Half Adder
- It is a basic building block for adding two single-bit binary numbers.
- It has two inputs (A and B) and two outputs: Sum (S) and Carry (C).
- The Sum (S) output represents the result of the addition operation, and the Carry (C) output represents a possible carry-over bit.
Full Adder
- It is used to add three single-bit binary numbers (A, B, and Cin, where Cin is a carry-in from a previous addition).
- It has three inputs (A, B, and Cin) and two outputs: Sum (S) and Carry (C).
- The Sum (S) output represents the result of the addition operation, and the Carry (C) output represents a possible carry-over bit.
Binary Adder
- A binary adder is used to add two binary numbers with multiple bits.
- Common examples include 4-bit binary adders which add two 4-bit numbers.
- The addition is performed in parallel using a series of half adders and full adders.
BCD Adder
- It is a specialized adder designed to add binary coded decimal (BCD) numbers.
- BCD represents decimal numbers using 4-bit binary codes.
- A standard binary adder cannot directly add BCD numbers because the BCD representation of numbers higher than 9 differs from their binary representation.
- A BCD adder uses a correction factor (addition of 6) after every addition to ensure the correct BCD output.
Subtractor
- Subtraction of binary numbers can't be directly implemented using basic logic gates, so alternative methods using complement representation are employed.
Subtraction Using 1's Complement
- The 1's complement of a binary number is created by inverting each bit (changing 0s to 1s and vice versa).
- Subtraction is achieved by adding the 1's complement of subtrahend to the minuend.
- An end-around carry needs to be added to the result if a carry-out occurs.
Subtraction Using 2's Complement
- The 2's complement of a binary number is calculated by adding 1 to its 1's complement.
- Subtraction is achieved by adding the 2's complement of the subtrahend to the minuend.
- No end-around carry is needed in this method.
Half Subtractor
- A half subtractor is a circuit designed to perform subtraction of two single-bit binary numbers.
- It has two inputs (A and B) and two outputs: Difference (D) and Borrow (B).
- The Difference (D) output represents the difference between the two inputs, and the Borrow (B) output represents a possible borrow bit needed for the next stage of subtraction.
Full Subtractor
- A full subtractor is used to perform subtraction of three single-bit binary numbers.
- It has three inputs (A, B, and Bin, where Bin is a borrow-in from a previous subtraction) and two outputs: Difference (D) and Borrow (B).
- The Difference (D) output represents the difference between the inputs, and the Borrow (B) output represents a possible borrow bit needed for the next stage of subtraction.
Comparator
- A comparator circuit is designed to compare two binary numbers or bits.
- It provides outputs indicating the relationship between the numbers: equal, not equal, greater than, less than.
- Comparators are used in control systems, data sorting circuits, and other digital applications.
Multiplexer (MUX)
- A multiplexer is a circuit that selects one of multiple input signals and forwards it to a single output.
- It acts like a switch that chooses which input signal is passed through.
- The selection of the input is controlled by a set of data select (DS) control inputs.
- Multiplexers are used in data routing, address decoding, and other digital systems.
Demultiplexer (DEMUX)
- A demultiplexer is a circuit with one input and multiple outputs.
- It routes the single data input to one of the outputs based on the value of select input.
- Only one output is enabled at a time, receiving the data input while the rest remain at logic 0.
- Demultiplexers are commonly used in communication systems and memory addressing.
Encoder
- An encoder is a combinational logic circuit that converts data from one format (usually a set of inputs) to another (usually a binary code).
- It is a reverse operation of a decoder.
- It has multiple inputs and fewer outputs.
- Examples include priority encoders which prioritize the highest-valued input.
Decoder
- A decoder is a combinational logic circuit that converts a binary input code to a specific output signal.
- It is a circuit with n input lines and 2n output lines.
- Only one output is enabled at a time, corresponding to the specific binary code input.
- Decoders are commonly used in memory addressing, code conversion, and other digital systems.
Binary Code
- A binary code is a system of representing data using only two symbols, 0 and 1.
- It is the fundamental basis of digital electronics.
- Various types of binary codes are used to represent numbers, letters, and symbols.
Weighted Codes
- In weighted codes, each bit position in a codeword has a specific weight.
- The decimal value of the code is obtained by multiplying each bit with its corresponding weight and adding the results.
- Example: BCD (Binary Coded Decimal)
Binary Coded Decimal (BCD) Code
- BCD code uses 4 bits to represent each decimal digit.
- Each BCD digit is equivalent to its corresponding decimal value.
- BCD codes are used in systems where decimal representation is desired.
Non-Weighted Code
- In non-weighted codes, the bit positions do not have assigned weights.
- Examples include Excess-3 code and Gray code.
Excess-3 Code
- An Excess-3 code is a non-weighted code in which each decimal digit is represented by its binary equivalent plus 3.
- It is used for addition and subtraction.
- It also helps in error detection.
Gray Code
- A Gray code is a non-weighted code where only one bit changes between sequential numbers.
- It is used in systems that require smooth transitions between states, such as shaft position encoders.
- It is also used in data-driven systems where a single bit change can cause an issue.
Conversion
- Binary to Decimal: The decimal equivalent of a binary number is calculated by multiplying each bit position in the binary number by its corresponding power of 2 and adding the results.
- Decimal to Binary: The decimal number is repeatedly divided by 2, and the remainders are collected in reverse order to form the binary equivalent.
- BCD to Decimal: Each BCD digit is converted individually from its binary representation to its decimal equivalent.
- Decimal to BCD: The decimal number is converted to its binary equivalent, and then represented using 4-bit binary codes for each decimal digit.
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