How do transistors translate into computations?

Question

I do not understand how transistors are used to compute, especially how immense amounts of them are used, how does what know the states of all of them?

In: 1

Answer 1

Transistors in various configurations can mimic the behavior of what we call logical “gates.”

Logical gates take, as input, logical values (True or False) and output a logical value (True or False). Examples include the NOT gate (which takes True or False and outputs the opposite value; True > False, False > True), AND gate (which outputs True only if both of its two inputs are True and False otherwise), and the OR gate (which outputs False only if both of its two inputs are False and True otherwise). There are others, but these are the basic ones.

Transistors can mimic the behavior using High and Low voltages to represent True and False, respectively. You can use a Transistor to act as a NOT gate by output a High voltage when the input is Low and vice versa. You can use Transistors in parallel or serial to mimic AND and OR gates, and all the other gates not mentioned.

So we can implement, electronically, logical gates, by interpreting High and Low voltages as True or False values. We can also extend this to math.

If you look at single bit binary addition we have the following possibilities:

0 + 0 = 00

1 + 0 = 01

0 + 1 = 00

1 + 1 = 10

If we interpret 1’s and 0’s as True and False, respectively, we can interpret this as a logical operation. The left-most digit of the output behaves as an AND gate (only outputs 1/TRUE if both inputs are 1/TRUE) and the right-most digit of the output behaves as what is known as a XOR (exclusive or) gate (only outputs 1/TRUE if either, but *not* both inputs are 1/True).

Since we can represent binary addition via logical gates, and since we can represent logical gates using transistors we can now perform binary addition with transistors.

And this extends to all sorts of mathematical operations (inverting, adding, subtracting, multiplication, division, comparison), logical operations (NOT, AND, OR, etc. on multiple arrays of bits), and other kinds of manipulations (shifting bits to the left or right).