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@ -8,7 +8,7 @@ tags: [electricity, electrical-circuits]
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An electrical circuit is a set of electrical components connected in such a way that current flows in a loop from a voltage source, through the circuit elements and back to the voltage source.
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Below is a basic circuit representing a 9-volt [battery](/Electronics_and_Hardware/Analogue_circuits/Cells_and_batteries.md#cells-and-batteries) with a 10,000$\Omega$ [resistor](/Electronics_and_Hardware/Analogue_circuits/Resistance.md) attached accross its terminals. Through the application of [Ohm's Law](/Electronics/Physics_of_electricity/Ohms_Law.md) we can determine that the maximum current will be 0.9 miliamps.
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Below is a basic circuit representing a 9-volt [battery](/Electronics_and_Hardware/Analogue_circuits/Cells_and_batteries.md#cells-and-batteries) with a 10,000$\Omega$ [resistor](/Electronics_and_Hardware/Analogue_circuits/Resistance.md) attached accross its terminals. Through the application of [Ohm's Law](/Electronics_and_Hardware/Physics_of_electricity/Ohms_Law.md) we can determine that the maximum current will be 0.9 miliamps.
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@ -14,9 +14,9 @@ So current is the flow of electrons. Charge is the quantity that flows.
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## Why current exists
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Current exists because of the [first law of electrostatics](/Electronics/Physics_of_electricity/Coulombs_Laws.md).
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Current exists because of the [first law of electrostatics](/Electronics_and_Hardware/Physics_of_electricity/Coulombs_Laws.md).
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When there is an excess of electrons at one terminal (i.e. negatively charged atoms) and a deficiency of electrons at the other terminal (i.e. positively charged atoms), a [_difference of potential_](/Electronics/Voltage.md) exists between the two terminals.
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When there is an excess of electrons at one terminal (i.e. negatively charged atoms) and a deficiency of electrons at the other terminal (i.e. positively charged atoms), a [_difference of potential_](/Electronics_and_Hardware/Analogue_circuits/Voltage.md) exists between the two terminals.
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When the terminals are connected to each other via a conductor (e.g. copper wire) electrons will flow along the conductor. This is provided that there is a source to supply electrons at one end and remove them at the other. We call this force the **voltage source**.
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@ -14,4 +14,4 @@ A **diode** is a special kind of component that only permits current to flow thr
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An LED diode lights up when the right amount of current flows through it. A standard LED has a maximum current of 20mA. An appropriate [resistor](/Electronics/Resistance.md#resistors) must therefore be added to the circuit to ensure the current doesn't exeedd this amount.
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An LED diode lights up when the right amount of current flows through it. A standard LED has a maximum current of 20mA. An appropriate [resistor](/Electronics_and_Hardware/Analogue_circuits/Resistance.md#resistors) must therefore be added to the circuit to ensure the current doesn't exeedd this amount.
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@ -25,7 +25,7 @@ Resistance and insulation are not the same thing although they relate to the sam
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- We use $R$ to represent resistance
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- The unit of resistance is **ohms** ($\Omega$)
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> One ohm is the resistance of a circuit or circuit element that permits a steady current flow of one [amp](/Electronics/Current.md#formal-expression) (one coulomb/second) when one [volt](/Electronics/Physics_of_electricity/Voltage.md#voltage) is applied to the circuit.
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> One ohm is the resistance of a circuit or circuit element that permits a steady current flow of one [amp](/Electronics_and_Hardware/Analogue_circuits/Current.md#formal-expression) (one coulomb/second) when one [volt](/Electronics_and_Hardware/Analogue_circuits/Voltage.md#voltage) is applied to the circuit.
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### Conductance
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## Ohm's Law
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The relationship between current, resistance and voltage is expressed in [Ohm's Law](/Electronics/Physics_of_electricity/Ohms_Law.md).
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The relationship between current, resistance and voltage is expressed in [Ohm's Law](/Electronics_and_Hardware/Physics_of_electricity/Ohms_Law.md).
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## Resistors
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## Difference of potential and the tranfer of energy
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We noted in the discussion of [current](/Electronics/Current.md) that current flows when there is a difference of potential between two points with negatively charged atoms at one point and positively charged atoms at the other.
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We noted in the discussion of [current](/Electronics_and_Hardware/Analogue_circuits/Current.md) that current flows when there is a difference of potential between two points with negatively charged atoms at one point and positively charged atoms at the other.
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_Difference of potential_ is the same thing as voltage. Voltage is essential to current because it is the force that enables the current to flow.
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Without voltage there can be no current because in their natural state, the electrons in an atom are in random motion with no direction. To produce a current, energy must be imparted to the electrons so that they all flow in the same direction.
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Voltage is the application of this energy. Any [form of energy](/Electronics/Voltage_sources.md) that dislodges electrons from atoms can be used to produce current. Thus:
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Voltage is the application of this energy. Any [form of energy](/Electronics_and_Hardware/Analogue_circuits/Voltage_sources.md) that dislodges electrons from atoms can be used to produce current. Thus:
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> Voltage is the work required per coulomb to move a charge from one point to another.
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### Voltage exists even without current
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Given that voltage is the force that generates current, it would be natural to think that voltage only exists when a voltage source (such as a [battery](/Electronics/Cells_and_batteries.m`)) is connected to a circuit. This however is not the case. Even if a 9V battery isn't connected to anything it still has a difference of potential of 9-volts accross its terminals. Remember voltage is _potential energy_ not just the actualisation of that energy.
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Given that voltage is the force that generates current, it would be natural to think that voltage only exists when a voltage source (such as a [battery](/Electronics_and_Hardware/Analogue_circuits/Cells_and_batteries.md)) is connected to a circuit. This however is not the case. Even if a 9V battery isn't connected to anything it still has a difference of potential of 9-volts accross its terminals. Remember voltage is _potential energy_ not just the actualisation of that energy.
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## Voltage rise and voltage drops
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The explanation for the voltage drop at the positions $V^{A}$ and $V^{D}$ are obvious enough: they are at the beginning and end of the loop so are equal to the maximal voltage rise and minimal voltage drop, respectively.
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We can work out the voltage of the remaining voltage points by inverting [Ohm's Law](/Electronics/Physics_of_electricity/Ohms_Law.md): $V = I \times R$:
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We can work out the voltage of the remaining voltage points by inverting [Ohm's Law](/Electronics_and_Hardware/Physics_of_electricity/Ohms_Law.md): $V = I \times R$:
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For the voltage at $V^{B}$:
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@ -37,7 +37,7 @@ Depending on how it is wired, a generator can produce **directed current** (DC)
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### Chemicals (cells and batteries)
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The chemical creation of current is the physics behind [batteries](/Electronics/Cells_and_batteries.md). Chemical current production produces currents on a smaller and less industrial scale than generators.
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The chemical creation of current is the physics behind [batteries](/Electronics_and_Hardware/Analogue_circuits/Cells_and_batteries.md). Chemical current production produces currents on a smaller and less industrial scale than generators.
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A chemical cell consists in two dissimilar metals such as copper and zinc. We call these the **electrodes**. They are immersed in a salt, acid or alkaline solution. We call these the **electrolytes**. The electrolyte pulls the free electrons from the copper electrode which leaves it imbalanced with a positive charge. The zinc electrode attracts the free electrons from the electrolyte giving it a negative charge, thus a difference of potential is achieved.
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Solar energy can be converted to electrical energy through solar panels which are large collections of **photovoltaic cells**.
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When the surfaces of these cells are exposed to light, it dislodges electrons from their orbits around the surface atoms of the cell material. For each cell this only produces a very small amount of energy, therefore large quantities must be used.
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[a new link](/Data_Structures/Arrays.md)
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## Binary prefix
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To distinguish numbers in binary from decimal or [hexadecimal](/Hardware/Binary/Hexadecimal_number_system.md) numbers, it is common to use the prefix `0b`. Thus, e.g, `0b110` for decimal `6`.
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To distinguish numbers in binary from decimal or [hexadecimal](/Electronics_and_Hardware/Binary/Hexadecimal_number_system.md) numbers, it is common to use the prefix `0b`. Thus, e.g, `0b110` for decimal `6`.
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## Converting decimal to binary
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A single place or symbol in a decimal number is called a **digit**. For example the number 343 is a number containing three digits. A digit can be any numeral through 0-9.
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The equivalent entity in the [binary number system](/Hardware/Binary/Binary_number_system.md) is the **bit**. For example the binary number 110 has three bits. A bit can only have one of two values in contrast to a digit which can have one of ten values: 0 or 1.
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The equivalent entity in the [binary number system](/Electronics_and_Hardware/Binary/Binary_number_system.md) is the **bit**. For example the binary number 110 has three bits. A bit can only have one of two values in contrast to a digit which can have one of ten values: 0 or 1.
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## Sequences of bits
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## Metric units: kilobytes, megabytes etc
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Having established that the core quantity of information is the byte, the convention is to apply the [standard metric prefixes](/Electronics/Prefixes_for_units_of_electrical_measurement.md) to the byte to establish units:
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Having established that the core quantity of information is the byte, the convention is to apply the [standard metric prefixes](/Electronics_and_Hardware/Prefixes_for_units_of_electrical_measurement.md) to the byte to establish units:
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| Prefix | Symbol | Expression as base ten exponent | Value | English word |
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| ------ | ------ | ------------------------------- | ----------------- | ------------ |
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# Hexadecimal number system
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Hexadecimal is the other main number system used in computing. It works in tandem with the [binary number system](/Hardware/Binary/Binary_number_system.md) and provides an easier and more accessible means of working with long sequences of binary numbers.
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Hexadecimal is the other main number system used in computing. It works in tandem with the [binary number system](/Electronics_and_Hardware/Binary/Binary_number_system.md) and provides an easier and more accessible means of working with long sequences of binary numbers.
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## Hexadecimal place value
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# Binary encoding of colours
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The approach to encoding binary representations of colour is very similar to the approach we explored when looking at the encoding of [alphanumeric values](/Hardware/Binary/Text_encoding.md).
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The approach to encoding binary representations of colour is very similar to the approach we explored when looking at the encoding of [alphanumeric values](/Electronics_and_Hardware/Binary/Text_encoding.md).
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We begin by determining the total number of colours and colour shades we want to represent. With this value established we then decide on the bit-length required that will accomodate this number of variations. Finally, we assign a binary number to each representation.
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### Advantages
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The chief advantage of the two's complement technique of signing numbers is that its circuit implementation is no different from the adding of two unsigned numbers. Once the signing algorithm is applied the addition can be passed through an [adder](/Electronics/Digital_Circuits/Half_adder_and_full_adder.md) component without any special handling or additional hardware.
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The chief advantage of the two's complement technique of signing numbers is that its circuit implementation is no different from the adding of two unsigned numbers. Once the signing algorithm is applied the addition can be passed through an [adder](/Electronics_and_Hardware/Digital_circuits/Half_adder_and_full_adder.md) component without any special handling or additional hardware.
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Let's demonstrate this with the following addition:
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Which is 4. This means the calculation above would be identical whether we were calculating $7 + -3$ or $7 + 13$.
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The ease by which we conduct signed arithmetic with standard hardware contrasts with alternative approaches to signing numbers. An example of another approach is **signed magnitude representation**. A basic implemetation of this would be to say that for a given bit-length (6, 16, 32...) if the [most significant bit](/Electronics/Digital_Circuits/Half_adder_and_full_adder.md#binary-arithmetic) is a 0 then the number is positive. If it is 1 then it is negative.
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The ease by which we conduct signed arithmetic with standard hardware contrasts with alternative approaches to signing numbers. An example of another approach is **signed magnitude representation**. A basic implemetation of this would be to say that for a given bit-length (6, 16, 32...) if the [most significant bit](/Electronics_and_Hardware/Digital_circuits/Half_adder_and_full_adder.md#binary-arithmetic) is a 0 then the number is positive. If it is 1 then it is negative.
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This works but it requires extra complexity to in a system's design to account for the bit that has a special meaning. Adder components would need to be modified to account for it.
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# Text encoding
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Text encoding is an applied instance of [binary encoding](/Hardware/Binary/Binary_encoding.md).
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Text encoding is an applied instance of [binary encoding](/Electronics_and_Hardware/Binary/Binary_encoding.md).
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## ASCII
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# Digital circuits
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Ultimately every process in a computer is the product of a digital [circuit](/Electronics/Circuits.md) that is working on binary values. In contrast to electrical circuits, digital circuits are not represented in an [analogue](/Hardware/Analogue_and_digital.md) fashion.
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Ultimately every process in a computer is the product of a digital [circuit](/Electronics_and_Hardware/Analogue_circuits/Circuits.md) that is working on binary values. In contrast to electrical circuits, digital circuits are not represented in an [analogue](/Electronics_and_Hardware/Analogue_and_digital.md) fashion.
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Analogue circuits work on the basis of real continuous phenomena in the world: charges and currents. As a result, the key properties of a circuit - voltage, current and resistance - can vary over a wide range of values. This is the reason that we require components like batteries and resistors: to control the natural flow of current and ensure that it only runs within desired parameters.
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In a standard electrical circuit, voltage, current and resistance can vary over a wide range of values however in the binary context we want to deal with discrete values (zeros and ones) which can be fed into the various [logic gates](/Hardware/Logic_Gates/Logic_gates.md).
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In a standard electrical circuit, voltage, current and resistance can vary over a wide range of values however in the binary context we want to deal with discrete values (zeros and ones) which can be fed into the various [logic gates](/Electronics_and_Hardware/Logic_gates/Logic_gates.md).
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We therefore need a way to represent 'on' and 'off' as single quantities. We do this by stipulating that a given voltage corresponds to 'on' (high) and another corresponds to 'off' (low). Of course these are not really discrete values since voltage is inherently analogue but we basically binary-encode them. Formally 'on' has a voltage of 1 and 'off' has a voltage of 0. In reality 'on' tends to be within 2-5V depending on the circuit design and anything between 0 - 0.8V is considered off.
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The [transistor](/Electronics/Switches_and_transistors.md) is the electrical component that enables us to represent given voltage ranges as being 'on' or 'off'.
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The [transistor](/Electronics_and_Hardware/Digital_circuits/Transistors.md) is the electrical component that enables us to represent given voltage ranges as being 'on' or 'off'.
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# Four-bit adder
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A single [half adder](/Electronics/Digital_Circuits/Half_adder_and_full_adder.md#half-adder) and [full adder](/Electronics/Digital_Circuits/Half_adder_and_full_adder.md#fufll-adder) allows us to calculate the sum of two 1-bit numbers, but this is not much use in practice. To approximate what is really happening at the circuit level in computers we need to be able to add bigger binary numbers. We will demonstrate how this can be achieved for a four-bit number (nibble) using repeated full adders and half adders.
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A single [half adder](/Electronics_and_Hardware/Digital_circuits/Half_adder_and_full_adder.md#half-adder) and [full adder](/Electronics_and_Hardware/Digital_circuits/Half_adder_and_full_adder.md#fufll-adder) allows us to calculate the sum of two 1-bit numbers, but this is not much use in practice. To approximate what is really happening at the circuit level in computers we need to be able to add bigger binary numbers. We will demonstrate how this can be achieved for a four-bit number (nibble) using repeated full adders and half adders.
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We want to be able to calculate the following sum:
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| 1 | 0 | 1 | 0 |
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| 1 | 1 | 0 | 1 |
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We can see that the sum bit column replicates the truth-conditions of [XOR](/Hardware/Logic_Gates/Xor_gate.md):
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We can see that the sum bit column replicates the truth-conditions of [XOR](/Electronics_and_Hardware/Logic_gates/Logic_gates.md#xor-gate):
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| P | Q | P V Q |
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| --- | --- | ----- |
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| F | T | T |
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| F | F | F |
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And the carry-out bit replicates the truth conditions of [AND](/Hardware/Logic_Gates/And_gate.md):
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And the carry-out bit replicates the truth conditions of [AND](/Electronics_and_Hardware/Logic_gates/Logic_gates.md#and-gate):
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| P | Q | P & Q |
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| --- | --- | ----- |
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# Integrated circuits
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An integrated circuit (IC) is a single unit that comprises several logic gates designed for the easy construction of [digital circuits](/Electronics/Digital_Circuits/Digital_circuits.md). The terms "integrated circuit" and "chip" are often used interchangeably.
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An integrated circuit (IC) is a single unit that comprises several logic gates designed for the easy construction of [digital circuits](/Electronics_and_Hardware/Digital_circuits/Digital_circuits.md). The terms "integrated circuit" and "chip" are often used interchangeably.
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An IC puts the gates on a single piece of silicon that has electrical contact points called pins. The type we will look at are called **dual in-line packages** (DIPs). They are rectangular wth two parallel rows of pins. The pins make it easy to connect DIPs to a breadboard.
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# Latches
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The combinatorial digital circuits we have looked at so far have been non-sequential. The outcome is a function of its immediate set of inputs and everything happens at once: there is no means of storing state for future use. In other words there is no _[memory](/Hardware/Memory/Memory.md)_.
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The combinatorial digital circuits we have looked at so far have been non-sequential. The outcome is a function of its immediate set of inputs and everything happens at once: there is no means of storing state for future use. In other words there is no _[memory](/Computer_Architecture/Memory/Memory.md)_.
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In contrast, a sequential digital circuit's output depends not only on its present set of inputs but also on past inputs to the circuit. It has some knowledge of its own previous state through the existence of memory. This can be implemented via components that allow for the **storage and retrieval of binary data**.
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## Creating a latch circuit
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The circuit diagram latch symbol obviously encapsulates more complex functionality that occurs at the sub-circuit level. We will demonstrate how this functionality can be achieved with two [NOR](/Hardware/Logic_Gates/Logic_gates.md#nor-gate) gates.
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The circuit diagram latch symbol obviously encapsulates more complex functionality that occurs at the sub-circuit level. We will demonstrate how this functionality can be achieved with two [NOR](/Electronics_and_Hardware/Logic_gates/Logic_gates.md#nor-gate) gates.
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The two gates are in a **cross-coupled configuration**. This basically means that the wires are crossed back on themselves such that the output of one is also an input of the other at a single stage in the sequence.
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# Transistors
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In the discussion of [digital circuits](/Electronics/Digital_Circuits/Digital_circuits.md) we noted that a digital circuit requires that electrical phenomena be treated as discrete rather than continuous values. Although a given voltage at a point in the circuit can vary widely, in order to represent the binary states of 'on' and 'off' we need it to remain fixed within certain narrow parameters. Typi>understanding the concept and then with transistors which are what are actually used in computers.
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In the discussion of [digital circuits](/Electronics_and_Hardware/Digital_circuits/Digital_circuits.md) we noted that a digital circuit requires that electrical phenomena be treated as discrete rather than continuous values. Although a given voltage at a point in the circuit can vary widely, in order to represent the binary states of 'on' and 'off' we need it to remain fixed within certain narrow parameters. Typi>understanding the concept and then with transistors which are what are actually used in computers.
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## Implementing binary logic with mechanical switches
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In real digital circuits, mechanical switches would be totally impractical. The number of switches required is too numerous and we need to be able to connect and interconnect the output of many circuits together. The output of one circuit needs to be fed into another and there is no way to do this with switches.
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Thus instead of switches, modern digital circuits use transistors, a special electrical component that controls the flow of current in the manner of a switch where the 'off' and 'on' states are represented by [voltage](/Electronics/Voltage.md) values within set parameters.
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Thus instead of switches, modern digital circuits use transistors, a special electrical component that controls the flow of current in the manner of a switch where the 'off' and 'on' states are represented by [voltage](/Electronics_and_Hardware/Analogue_circuits/Voltage.md) values within set parameters.
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There are different types of transistors but the simplest for the purposes of explanation are **bipolar junction transistors**.
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@ -58,10 +58,10 @@ When the voltate at the base is low (in the diagram it is grounded to ensure thi
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With the basic element of the transistor established, we can combine transistors to create logic gates. A logic gate is a combination/sequence of transistors where the logical function is represented by the characteristic input and output voltages.
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For example to create an [AND](/Hardware/Logic_Gates/And_gate.md) gate we would have two voltage inputs going into two transistors that are connected in sequence. The two transistors create a continuous line going from the collector of one to the emitter of the other. If either voltage input is low then the voltage of the combined line is low (equivalent to the circuit being broken) and there is no current flowing.
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For example to create an [AND](/Electronics_and_Hardware/Logic_gates/Logic_gates.md#and-gate) gate we would have two voltage inputs going into two transistors that are connected in sequence. The two transistors create a continuous line going from the collector of one to the emitter of the other. If either voltage input is low then the voltage of the combined line is low (equivalent to the circuit being broken) and there is no current flowing.
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Below, an [OR](/Hardware/Logic_Gates/Or_gate.md) has been constructed with transistors. If a voltage is applied to the base of either transistor, the current reaches the V-out terminal.
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Below, an [OR](/Electronics_and_Hardware/Logic_gates/Logic_gates.md#or-gate) has been constructed with transistors. If a voltage is applied to the base of either transistor, the current reaches the V-out terminal.
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Reference in a new issue