Digital Circuits Flashcards
Reversible 3-bit binary to gray code converter (or gray code to binary converter… same circuit either way)
Enable
The “Enable” signal is used in digital circuits to control whether a specific operation or part of the circuit is active.
* When the enable signal is high (logic 1), the circuit or operation is allowed to proceed.
* When the enable signal is low (logic 0), the circuit is disabled, preventing any changes to its state.
Reset
The “Reset” signal is used to initialize or reset a digital system to a known state, usually bringing it back to zero or a default condition. This is essential in ensuring that a circuit starts from a predictable state when powered on or after an error condition.
- Often modeled using a finite state machine
Overflow Alert
The “Overflow Alert” is a signal or flag used in arithmetic circuits (like adders) to indicate when the result of an operation exceeds the available range of the system. For example, in a binary addition, an overflow occurs when the sum exceeds the maximum value that can be represented by the given number of bits.
Clock Signal
The “Clock Signal” is a periodic square wave used to synchronize operations in SEQUENTIAL logic circuits. It provides a timing reference for operations like data transfers, state changes, and triggering other events at regular intervals.
Full Adder
A “Full Adder” is a digital circuit that adds two binary digits and a carry-in bit. It produces a sum and a carry-out. It takes three inputs (two bits to be added and a carry-in from the previous addition) and outputs the sum and carry. Full adders are used in constructing larger adders for multi-bit binary numbers.
Half Adder
A “Half Adder” is a digital circuit that adds two single binary digits, producing a sum and a carry-out. Unlike the full adder, it doesn’t account for carry-in from a previous addition. It only works with two inputs, making it suitable for adding the least significant bits in multi-bit addition.
Carry-over signal
A carry-over signal (also called carry-out) in digital logic is a signal generated during arithmetic operations, specifically addition, when the sum of two or more binary digits exceeds the value that can be represented by a single bit.
An adder circuit could have many internal carry signals
2-bit Binary Full Adder
2-bit binary full Adder
3-bit binary to gray code converter
This is also reversible (meaning that it can work as a 3-bit gray-code to binary converter)
Flip Flops
Flip-flops are basic memory elements in digital circuits. Each one can store data, but only a single bit (either 0 or 1). Sequential logic circuits are composed of networks of flipflops.
Components: Can be constructed from latches with additional logic gates (AND, OR, NOT).
Function: A flip-flop is a more complex memory device that stores a single bit of data and changes its state on a clock edge (either rising or falling). This allows it to be used in synchronous circuits.
Use: Flip-flops are the building blocks for registers, counters, and memory in digital systems. They store and synchronize data in sequential circuits.
Types:
SR Flip-Flop: Built from an SR latch with a clock input.
D Flip-Flop: A D latch with clock synchronization, where the output follows the input on the clock edge.
JK Flip-Flop: A modification of the SR flip-flop with feedback, eliminating the indeterminate state. It toggles the stored bit based on inputs.
T Flip-Flop: A toggle flip-flop, often derived from a JK flip-flop, which switches between 0 and 1 on each clock pulse.
Counters
Counters are sequential digital circuits used to count events, time, or cycles. They are made up of a series of flip-flops connected in a specific sequence and can count up (up-counters), down (down-counters), or both (up/down counters). Examples include the 74LS90 (a 4-bit binary counter) or 74LS393 (a dual 4-bit counter).
Multiplexers
Multiplexers are digital devices used to select one of several input signals and forward the chosen input to a single output line. They function as data selectors.
Demultiplexors
Demultiplexers do the reverse of multiplexers by taking a single input and routing it to one of several outputs. They are used in data distribution and digital display systems.
Decoders
Decoders are used to convert binary information from ‘n’ input lines into a maximum of 2ⁿ unique output lines. They are used in memory address decoding, and display drivers [verify]
Encoders
Encoders do the opposite of decoders by converting 2ⁿ inputs into a binary number of ‘n’ bits. They are used in situations where you need to reduce the number of signal lines, like keypad encoders.
Digital Comparators
Combinational logic circuit used to compare two binary numbers and determine their relative magnitude. It outputs whether one number is greater than, less than, or equal to the other.
Types of Comparators:
1) 1-bit Comparator: Compares two single-bit binary inputs and outputs whether A > B, A < B, or A = B.
2) Multi-bit Comparator: Compares multi-bit binary numbers (e.g., 4-bit or 8-bit) to provide the same relational results.
Applications:
1) ALUs (Arithmetic Logic Units): For decision-making in microprocessors.
Sorting Circuits: To arrange numbers in order.
2) Control Systems: To regulate processes based on comparisons.
Structure:
Comparators use AND, OR, and NOT gates to compare the bits of the two numbers from the most significant to the least significant bit.
Digital-to-Analog Converter
A Digital-to-Analog Converter (DAC) is a device that converts digital signals, usually binary, into an analog signal, typically voltage or current. This is important in systems where digital processors (which handle binary data) need to interact with real-world analog components (such as speakers, sensors, or communication systems).
Key Features of DACs:
- Resolution: The number of bits in the digital input (e.g., 8-bit, 12-bit) determines the precision of the analog output.
- Conversion Speed: How fast the DAC can convert digital data into an analog signal.
- Output Type: DACs typically produce voltage or current as output.
Applications:
Audio Systems: To convert digital audio files (e.g., MP3) into analog signals that can be played through speakers.
Video Systems: Convert digital video data into analog signals for display on screens.
Control Systems: Convert digital control signals to analog for motor control, sensor interfacing, or power regulation.
Types of DACs:
- Binary-Weighted DAC: Uses resistors with values weighted in powers of two to convert digital signals into analog.
- R-2R Ladder DAC: A more common type, using a resistor network of equal and double values (R and 2R).
- Sigma-Delta DAC: Converts high-resolution digital data into a stream of pulses, which are then filtered into a smooth analog signal.
Example:
An 8-bit DAC with an input range of 00000000 to 11111111 can produce 256 different voltage levels, with higher precision resulting from more bits.
DACs are essential in many digital systems for interfacing with the analog world, such as in sound reproduction, video output, communication systems, and industrial control systems.
Analog-to-Digital converter
An Analog-to-Digital Converter (ADC) is a device that converts continuous analog signals, like voltage or current, into discrete digital values. ADCs are essential for digital systems to process real-world analog inputs, such as temperature, sound, or light, by converting them into a format that microcontrollers or computers can understand.
Key Concepts:
- Resolution: Defines how many discrete levels the ADC can output, typically determined by the number of bits. A 10-bit ADC can output 1024 different values.
- Sampling Rate: Refers to how often the ADC samples the analog signal per second, usually measured in samples per second (SPS) or Hertz (Hz).
- Quantization: The process of mapping the continuous analog input to discrete digital values. This introduces quantization error, where some precision is lost.
- Types of ADCs:
Successive Approximation Register (SAR) ADC: One of the most common types, which converts the signal by approximating the input in binary steps.
Delta-Sigma ADC: Provides high accuracy by oversampling the signal and filtering noise.
Flash ADC: Very fast but typically lower in resolution, used in high-speed applications like oscilloscopes.
Application of ADCs:
Microcontrollers: Reading sensor data (e.g., temperature, light, etc.).
Audio Processing: Converting sound waves into digital signals for audio devices.
Communication Systems: Converting radio signals to digital data in modems or receivers.
ADCs are essential for integrating analog world signals into the digital domain.
Shift Registers
Shift registers are used to store and shift data bits serially or in parallel. They are widely used in data conversion between serial and parallel forms and in applications like LED matrix control.
Components: Built from a series of flip-flops connected in a chain.
Function: A shift register stores multiple bits of data and shifts them in one direction (serially or parallel). The data can be shifted left or right based on the input signal.
Use: Used in serial communication, data storage, and digital data manipulation.
Latches
Components: Built using NAND or NOR gates.
Function: A basic bistable memory element capable of storing a single bit of information. It has two inputs, Set and Reset, which control whether the stored bit is set to 1 or reset to 0.
Description:
When the Set input is triggered, the latch stores a logic 1.
When the Reset input is triggered, the latch stores a logic 0.
It can “latch” or hold a value until changed by one of the inputs.
Use: This is a fundamental element in memory and register circuits, forming the foundation of more complex storage devices.
Monostable Timer
Function: A monostable timer generates a single output pulse when triggered. After the pulse, it returns to its stable state and waits for the next trigger.
Use Case: It is used in applications where a fixed-duration pulse is needed in response to a trigger, such as in pulse-width modulation (PWM) or debouncing switches.
Astable Timer
Function: An astable timer has no stable state and continuously toggles between high and low, creating a periodic square wave. It acts as an oscillator.
Use Case: It is commonly used for generating clock signals, square waves, or PWM signals.
Bistable Timer
Function: A bistable timer has two stable states and can toggle between these states based on an external input signal. It stays in one state until an external event forces it into the other state.
Use Case: This is used in toggle switches, memory elements, and flip-flop circuits, where it remains in a state until an input triggers a change.
Retriggerable Timer
Function: A retriggerable timer extends the timing period each time it is retriggered before completing the current timing cycle. If it receives multiple triggers, it keeps extending the timing period.
Use Case: Used in watchdog timers and systems where a timeout resets if a specific signal is received within the time window.
Non-retriggerable Timer
Function: A non-retriggerable timer does not extend its timing period if it is retriggered during an ongoing cycle. It will ignore additional trigger inputs until the current timing cycle is complete.
Use Case: Used when only one fixed timing interval is desired, regardless of how many triggers occur within that interval.
Up/Down Timer
Function: An up/down timer can count either upwards or downwards based on control signals. The timer starts from a particular value and increases or decreases over time.
Use Case: These are commonly used in counters and frequency dividers, where you need to track the number of events, either incrementing or decrementing the count.
Real Time Clock
Function: A real-time clock keeps track of the current time and date in real-world units (seconds, minutes, hours, etc.). It maintains accurate time even when the system is powered off, using a backup power source like a battery.
Use Case: RTCs are used in systems requiring date and time information, such as digital clocks, scheduling systems, and embedded devices that keep track of time across power cycles.
Watchdog Timer
Function: A watchdog timer is used to reset a system if it fails to operate within a specified time interval. The system must periodically reset the watchdog timer; if it fails to do so, the timer will expire and generate a reset signal.
Use Case: Used in embedded systems and microcontrollers to prevent system crashes or hang-ups by automatically resetting the device if it stops responding.
Delay Timer
Function: A delay timer generates a delay between receiving an input and generating an output. The duration of the delay is determined by the configuration of the timer.
Use Case: These are used in circuits requiring a delayed response after an event, such as in power sequencing, motor start-up delays, or debouncing.
Pulsed Timer
Function: A pulsed timer generates a short pulse or a series of pulses after receiving a trigger. The duration of each pulse and the number of pulses can be controlled.
Use Case: These timers are used in pulse-generation circuits, such as pulse-width modulation (PWM) controllers, or to trigger a system with a defined pulse width.
555 Timer
The 555 timer is a widely-used integrated circuit (IC). It is extrememly versitle and can be configured to generate timing delays, pulses, or oscillations. It is known for its simplicity, versatility, and reliability, and it has been a fundamental component in electronics since its introduction in the 1970s.
Internal Structure:
The 555 timer consists of several components internally:
Two voltage dividers that divide the supply voltage.
Three resistors (hence “555”) forming a voltage reference.
Two comparators that compare input voltages.
A flip-flop that controls the output.
A discharge transistor to reset the timing capacitor.
Applications or Possible Roles
Pulse Timer: Used in motor speed control, light dimming, and audio signal generation.
Delay Timer: Used in creating precise delays for events, such as activating/deactivating a relay or producing a time-delayed response.
Astable Timer: Used in waveform generation, clock pulses for digital circuits, and tone generation.
Adders
Adders are used in arithmetic logic units (ALUs) to perform binary addition. A half-adder adds two single bits, while a full-adder adds three bits (two binary bits plus a carry-in). These circuits form the backbone of arithmetic computations in digital systems.
Finite State Machines
A state machine is a mathematical model of computation used to design both hardware and software systems. It represents a system with a finite number of states, and the system transitions between these states based on inputs or events.
Key Concepts of a State Machine:
States:
A state machine is always in one of its defined states at any given time. A state represents a specific condition or situation in which the system can exist.
Each state is associated with certain actions or outputs.
Transitions:
The machine changes from one state to another based on input conditions or events. These changes are called transitions.
Each transition is triggered by a specific condition or event (e.g., pressing a button, receiving a signal, etc.).
Inputs and Outputs:
Inputs are external signals or events that cause the state machine to transition between states.
Outputs are the actions or signals generated by the state machine depending on the current state.
Finite States:
State machines are often called finite state machines (FSMs) because they have a finite number of possible states. A state machine with infinite states would be difficult to control or design.
Applications of FSMs:
Digital Circuit Design: FSMs are used in sequential circuits like controllers, counters, and communication protocols. Protocol Design: FSMs are commonly used in defining communication protocols, where each state represents a phase of the communication process. Embedded Systems: In embedded systems, FSMs help design control logic for devices like washing machines, microwaves, and industrial machinery. Software Development: FSMs are used in game development, user interface design, and other applications requiring defined behavior based on inputs and events. Traffic Light Controllers: FSMs control traffic light sequences based on inputs from sensors or timers.
Programmable Logic Array
Components: Built using arrays of AND and OR gates.
Function: PLAs are used to implement combinational logic circuits and can store a combination of logic operations. They can be programmed by the user to store specific logic functions, much like memory for logic circuits.
Use: Used in hardware acceleration, custom logic, and control logic systems where reconfigurable logic is required.
ROM
Components: Built using a combination of AND, OR, and NOT gates to store fixed data that can be read but not changed.
Function: ROM stores data that cannot be modified after manufacturing (or programmed in the case of PROM). The stored data is permanently “burned” into the memory.
Description:
ROM is essentially a decoder where certain outputs are hardwired to store predefined values.
PROM, EPROM, and EEPROM variants allow some degree of reprogramming.
Use: Used in storing firmware, bootstrap loaders, or other data that needs to be retained permanently.
EEPROM
EEPROM is a type of digital memory device that can be electrically erased and reprogrammed. It is often used to store small amounts of data that must be saved when power is removed, like configuration settings.
SRAM
Components: Constructed from flip-flops (specifically, latches or D flip-flops).
Function: SRAM stores data in latches, maintaining the data as long as power is supplied. Each bit of data is stored in a separate latch or flip-flop, making it fast and easy to access.
Description: In 6-transistor (6T) SRAM cells, two cross-coupled inverters (acting as latches) store a bit, while additional transistors control reading and writing the data.
Use: SRAM is used in cache memory, register files, and other high-speed memory applications.
Example: Small SRAM blocks can be constructed using a combination of latches, pass gates, and logic gates for read/write control.
SR-Latch
An SR latch (Set-Reset latch) is a basic type of sequential logic circuit, often used in digital systems to store a single bit of information. It has two stable states (bistable) and can be set to either 1 or 0 depending on the inputs. The SR latch is constructed using two cross-coupled NOR or NAND gates, which creates feedback between the outputs, enabling the latch to “remember” its state.
Signals:
S (Set input): When this input is activated (typically set to 1), the latch sets its output to 1.
R (Reset input): When this input is activated, the latch resets its output to 0.
Q (Output): This is the primary output of the latch, representing the stored bit.
Q’ (Complementary output): This is the inverse of the Q output.
Application:
The SR latch is often used in memory elements, flip-flops, and circuits that require simple, bistable storage.
It can serve as the foundation for more complex storage devices like D flip-flops and JK flip-flops.
Working of an SR Latch:
Set condition (S = 1, R = 0): The output Q is set to 1 (latch is "set"). Reset condition (S = 0, R = 1): The output Q is reset to 0 (latch is "reset"). Hold condition (S = 0, R = 0): The output remains unchanged. Invalid condition (S = 1, R = 1): This is an indeterminate state for an SR latch based on NOR gates, leading to an undefined or unstable state (in SR latch using NAND gates, this condition forces both outputs to 0). In practical circuits, this condition is avoided.
Types of Flip-Flops
Mealy v. Moore State Machines
