Understanding Logic Gates transcript

inside your computer are billions of units called transistors these transistors serve a variety of purposes but they commonly act as a sort of very small light switch each switch can be turned on or turned off computer scientists will often represent a switch that's turned on with the number one and a switch that's turned off with the number zero these zeros and ones form a number system called binary and it's the fundamental language of computers from just these zeros and ones we end up with computers that can perform calculations create documents view images browse the web and more how does that happen in this series we'll explore the foundations of computer logic starting from the fundamentals and building our way to more and more sophisticated systems using these switches our computers can store information each switch stores a single bit of information a 0 or a 1 but computers don't just store information they process it transforming inputs into outputs that's where logic gates come in logic gates are the building blocks of computer circuits they accept input and produce output according to a set of logical rules one of the simplest logic gates is the not gate represented graphically here the not gate takes a single input either a 0 or a 1 and inverts it so that the output is the opposite of whatever the input is if the input is a 1 then the not gate outputs a 0 if the input is a 0 then the not gate outputs a 1 to represent the logical rule this gate obeys we can draw a truth table which is just a way of writing down the rules for some logical formula this table says that if the input is 0 then the output is 1 and if the input is 1 the output is 0 often though our computers need to be able to perform calculations not just on a single bit of information but on multiple bits of information the and gate shown here for example is a logic gate that takes two inputs instead of one let's call these two inputs a and B as the name might suggest the and gate will output a 1 when both a and B are ones but in all other cases and will output a 0 we can construct a truth table here too this truth table is a bit bigger since with two inputs there are more possibilities to consider if a and B are 0 the output is 0 if a is 0 and B is 1 the output is 0 if a is 1 and B is 0 the output is still 0 and only when both a and B are ones is the output a 1 the or gate meanwhile is also a logic gate that takes two inputs this gate outputs a 1 when a is a 1 or when B is a 1 so if both inputs are 0 the or gate outputs 0 but if either of the inputs is a 1 or both inputs are a 1 then the output of the or gate is also going to be a 1 these logic gates on their own follow fairly simple rules but they can combine with each other to form more complex calculations imagine what would happen if for example we took two inputs pass them into a NAND gate and then passed that output into a not gate what would happen if both inputs are 0 the and gate will output a 0 and the knot will turn that 0 into a 1 if only one of the inputs is a 0 nothing changes but if both inputs are 1 the and gate will output a 1 and the knot will turn that one into a 0 in other words this circuit appears to do the opposite of whatever the and gate on its own would do it turns out that inverting the result of an and calculation is such a common operation that it has its own logic gate the NAND gate this gate is equivalent to an and followed by a naught so if the and truth table looks like this then the NAND truth table is identical except all of the outputs are inverted whenever and when output is 0 mand outputs a 1 whenever and when I open a 1-man outputs a 0 as you might guess if there's a logic gate to take the opposite of a NAND gate there is also a logic gate that takes the opposite of an or gate this is the nor gate when both inputs are zero or would normally output a zero to so the nor gate will flip that and output a 1 in all other cases at least one of the inputs is 1 so or would output a 1 and so the nor gate will output a 0 instead let's now use these gates to solve a sample problem given two inputs a and B we'd like to calculate whether exactly one of them is a 1 well what does it mean logically for exactly one of these two inputs to be a 1 well it means that either A or B must be a 1 but it also means they can't both be a 1 so logically we might represent this as a or B and not a and B to mean that one of the two must be a 1 but both can't be a we could create a circuit to perform this calculation too but this circuit is starting to look fairly complex so once again there's a logic gate to solve this problem precisely the exclusive or gate outputs a 1 when exactly one of its inputs is a 1 so if only a is 1 or only B is 1 then the output of exclusive-or is 1 but otherwise if both inputs have the same value both zeros or both ones then the output is 0 and just for completeness sake there's also a gate for inverting the exclusive or gate the exclusive nor gate this gate does the opposite of what exclusive or does while exclusive or will output a one when the two inputs are different from each other exclusive nor will output a one when the two inputs are the same both zeros or both ones these illogical gates not and/or manned nor exclusive or and exclusive nor make up the foundation of computation in computers by combining just these few logical gates each of which obey is a relatively simple logical rule we can construct computers that can represent all of the data and perform all of the complex calculations that our computers do every day you