Transistor gate count8/2/2023 ![]() This requires two transistors, the inputs are on the bases and only if both inputs are one can the electricity flow to the output, making it a one also. If the input is zero, the transistor prevents the flow from collector to emitter, so the electricity flows out of the output causing it to be one. Since the electricity will always follow the path of least resistance the output will be zero. Here if the input is 1 it causes the electricity to flow from the collector to the emitter (top to bottom). Now let’s take a quick look at how we build logic gates using transistors. A 4-bit adder Building logic gates from transistors Since both the A and B inputs are now 4 bits we can add together 11 or 15 plus 15 in base 10 to get a five bit result. This picture shows a four bit adder, in fact, due to the way the carry bit ‘ripples’ down, this is known as a ripple carry adder. Now the simple full-adder logic circuits can be combined to allow bigger binary numbers to be added together. If you followed along with the half adder it’s pretty easy to see how this works from the logic diagram. This logic takes A, B and a carry as input and outputs the sum and carry. To solve this we combine two half-adders together to make a full-adder. This logic is called a ‘half-adder’ due to the fact that it is only capable of working on single bit numbers, since you cannot input the carry bit, you can’t cascade them together to work on larger binary numbers. To get the whole truth table we simply add the two logic circuits together. The carry output is even simpler, we want the carry to be 1 if both A and B is one, so we use an AND gate. If either gate outputs a 1 the result is 1 via the final OR gate. ![]() We can do this by simply using two AND gates with NOT gates on opposing inputs. Here we want the logic to output one only when one input is one and not the other, this is known as an exclusive OR gate. So, going back to our truth table, let’s look at the logic required to get ‘Sum’ based on the inputs A and B. Finally a NOT gate (or inverter as it is sometimes called) outputs the opposite of its input, so if the input is one the output is zero and vice-versa. An OR gate outputs one when either input is one. Basic Boolean operationsĪn AND gate outputs one only when both its inputs are one. You can make all other types of gates by combining these three. Here are the three basic types of logic gates which I’ve chosen because they are the simplest gates to make from transistors. In order to represent the ‘logic’ required to get from the possible range of inputs to the desired outputs we use Boolean operations, or as they are more commonly called in electronics, logic gates. Here you can see the 4 possible values of the inputs A and B, and the four possible outputs represented by Sum and Carry. ![]() It is useful to represent this in what’s known as a truth table. This means that if you have two single-figure binary numbers and you add them together there are only 4 possible results. Addition in Base 10īinary works exactly the same, however you carry over if the result is greater than 1, so one plus one equals one-zero. ![]() When we add numbers in base ten we carry over any digits which are greater than 9 into the next magnitude of units, so nine plus one equals zero carry one, or ten. So, for example 2 in base 10 is one- zero in base 2. However, it’s very similar, instead of ones, tens, hundreds and thousands, base 2 counts in ones, twos, fours, eights and so on. Since digital computers can only represent two states, on and off or zero and one, there are only two numbers available therefore they have to count in base 2, not base 10 as we would do. To begin with let’s have a look at some fundamentals. Thanks to reader for taking the time to review the logic diagrams! Fundamentals of binary counting Please note: There are a couple of mistakes on the slides in the youtube video which are shown corrected below. If you’ve ever wondered how electronic devices like computers can count, this article gives a simple introduction to binary and logic and shows how they are tied together with electronics to make both simple and complex computers.
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