History MediaNotes / BinaryLogic

'''NAND''': If all inputs are 1, the output is 0; the opposite of AND. This is one of the universal logic operations, which can create any other logic operation. Most commonly used in UsefulNotes/FlashMemory.

Note in this example for inputs 11, it produces the output 00, which makes Q = Q-not.

* Outside of computing, it's often written as "iff", for "if and only if", because one is true ''if and only if'' the other one is too.

'''XNOR''': Outputs a 1 if all inputs are the same value.

Below is a list of all the operations that can be done. All operations but "NOT" take in two inputs and spit out one output.

* For multi-input OR gates, outputs 1 if at least one input is 1.

'''AND''': Both inputs must be 1 for the output to be 1.

* For multi-input AND gates, outputs 1 if all inputs are 1.

'''XOR (Exclusive OR)''': Both inputs must be different for the output to be 1.

* For multi-input XOR gates, outputs 1 if there are an odd number of 1's.

'''NAND''': Same as the AND operation, but the output is inverted. One of the universal logic operations (you can do any of these operations with NAND gates). Most commonly used in UsefulNotes/FlashMemory.

* For multi-input NAND gates, outputs 0 if all inputs are 1.

'''NOR''': Same as the OR operation, but the output is inverted. The other universal logic operation.

* For multi-input NOR gates, outputs 0 if at least one input is 1.

'''XNOR''': Same as the XOR, but the output is inverted.

* For multi-input XNOR gates, outputs 1 if there are an even number of 1's.

'''Latch''': A latch is a fundamental "storage unit", made with a pair of NOR or NAND gates with the outputs feeding one of the other's inputs, as well as providing an actual output. This produces a pair of opposite outputs. Since there are two outputs, usually only one of them is used. The other can be used to avoid using a NOT gate if the signal's negative is needed. Latches also can produce an invalid result if its input is 00 or 11 depending on the type. This is due to the outputs equally each other when they should be different. If one of the inputs is a clock signal, a latch is called a flip-flop instead.

'''Latch''': A latch is a fundamental "storage unit", made with a pair of NOR or NAND gates with the outputs feeding one of the other's inputs, as well as providing an actual output. This produces a pair of opposite outputs. Since there are two outputs, usually only one of them is used. The other can be used to avoid using a NOT gate if the signal's negative is needed. Latches also can't have a certain input, which is either 00 or 11, depending on the type. If one of the inputs is a clock signal, a latch is called a flip-flop instead.

||Output (Q)|| (no change)|| 0|| 1|| (invalid)||
||Output (Q-not)|| (no change)|| 1|| 0|| (invalid)||

* Usually written using one or two [[ExactlyWhatItSaysOnTheTin ampersands]], '''⋅''' (dot operator) , or ∧

'''NAND''': Same as the AND operation, but the output is inverted. One of the universal logic operations (you can do any of these operations with NAND gates). Most commonly used in FlashMemory

* '''XNOR''': Same as the XOR, but the output is inverted.
** Outside of computing, it's often written as "iff", for "if and only if", because one is true ''if and only if'' the other one is too.
** For multi-input XNOR gates, outputs 1 if there are an even number of 1's.

For a typical set-reset latch, using output Q (as opposed to Q-not)

||Input || 00|| 01|| 10|| 11||

* '''NOT''': Inverts the incoming signal.
** Usually written as a leading exclamation mark or tilde.

* '''OR''': As long as one input is 1, the output is 1.
** Usually written using one or two pipe characters.
** Can be thought of as addition, only you have to believe for a moment that 1 + 1 = 1.
** For multi-input OR gates, outputs 1 if at least one input is 1.

* '''AND''': Both inputs must be 1 for the output to be 1.
** Usually written using one or two [[ExactlyWhatItSaysOnTheTin ampersands]]
** Can be thought of as multiplication.
** For multi-input AND gates, outputs 1 if all inputs are 1.

* '''XOR (Exclusive OR)''': Both inputs must be different for the output to be 1.
** Can be thought of subtraction, only the result is the always positive.
** For multi-input XOR gates, outputs 1 if there are an odd number of 1's.

* '''NAND''': Same as the AND operation, but the output is inverted. One of the universal logic operations (you can do any of these operations with NAND gates). Most commonly used in FlashMemory
** For multi-input NAND gates, outputs 0 if all inputs are 1.

* '''NOR''': Same as the OR operation, but the output is inverted. The other universal logic operation.
** For multi-input NOR gates, outputs 0 if at least one input is 1.

'''Three-state Buffer''': Normally, whatever signal comes into this will come out just the same. But there's a second input that when turned on, effectively "cuts off" the signal. This third state, known as the Hi-Z state, is seen by the rest of the system as disconnected.

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'''Latch''': A latch is a fundamental "storage unit", made with a pair of NOR or NAND gates with the outputs feeding one of the other's inputs, as well as providing an actual output. This produces a pair of opposite outputs. Since there are two outputs, usually only one of them is used. The other can be used to avoid using a NOT gate if the signal's negative is needed. Latches also can't have a certain input, which is either 00 or 11, depending on the type.

For a typical set-reset latch, using output Q (as opposed to Q-not)

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'''Flip-Flop''': A flip flop uses a type of latch that uses a clock signal as one of its inputs. Not only is it used to store information, but it can also be used to divide clock signals in half. There are three types of flip-flops named D, T, and JK. The D flip-flop sets its stored value to whatever its data input happens to be once per clock cycle. T and JK flip-flops are specialized and are not commonly used.

'''Latch''': A latch is a fundamental "storage unit", made with a pair of NOR or NAND gates with the outputs feeding one of the other's inputs, as well as providing an actual output. This produces a pair of opposite outputs. Since there are two outputs, usually only one of them is used. Latches also can't have a certain input, which is either 00 or 11, depending on the type.

'''Flip-Flop''': A flip flop uses a type of latch that uses a clock signal as one of its inputs. Not only is it used to store information, but it can also be used to divide clock signals in half. There are three types of flip-flops named D, T, and JK.