00:00We've learned about logic gates and identities, but how do we actually build something with them?
00:04In the digital world, we start with a Boolean function, a mathematical expression made of
00:10binary variables and operators like AND, OR, and NOT. Today, we're going to turn those equations
00:16into real-world circuits. A Boolean function takes binary variables as inputs and produces
00:22an output of either 0 or 1. For example, in the function f equals x plus y, the output is
00:280 only
00:29if both x and y are 0. For any other combination, the output is 1. Every algebraic expression like
00:36this can be transformed into a logic circuit. Let's start simple. To convert the function f1
00:42equals x, y, z, dr, we need a single AND gate for the term. But since we have a z
00:47-bar, we must first
00:48pass the z input through a NOT gate to invert it before it enters the AND gate. What if we
00:53have
00:53addition? For f2 equals x plus y, z, we use an AND gate for the y, z part and then
00:59feed that result
00:59along with x into an OR gate. For functions with multiple terms, like f4 equals x, r, y plus x,
01:07z,
01:07dr, we create individual branches. We use two AND gates for the two terms and two NOT gates to get
01:12our inverted inputs. Finally, an OR gate combines the outputs of both AND gates to give us our final
01:18result. No matter how long the function is, the process is the same. Solve the internal terms with
01:24AND gates and join them all together at the end with an OR gate. Want to try this yourself? You
01:29can
01:29use simulation tools like Logisim to build and test your own Boolean circuits before you ever pick up a
01:35soldering iron.
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