Created Wednesday 04 March 2020
minterm:
KMaps
Has a cell for each minterm.
kmap is essentially just a grid based on the truth table.
Groups are in powers of two.
From the kmap, we can derive a formula.
We can remove terms based on the groupings we see in the kmap.
7-segment display
Like what you see at baseball games. Yknow, the 8 thing?
To display numbers, we give input to the various components to only light up the portions of the number we want to display.
What if we can only turn on certain portions if certain segments are turned on?
Say, we need to turn on the f segments for the nubers, 0, 4, 5, and 6.
But the input will be arriving in three bit binary! 0 is 0 0 0. 4 is 1 0 0. 5 is 1 0 1. and 6 is 1 1 0.
Let's split this into p, q, and r. We can represent this all as a disjuntion (with the V or OR as you may know. Disjunction is just us ORing it all together.)
You can see a video of all this here.
Standard digital components are combined into single integrated circuit packages.
NAND Gates are cool :3
We can form any other gate with NAND gates as we say on Day 4.
Combinational Logic Circuit
produces a specified output (almost) at the instant when input values are applied
Such circuits are useful for many devices. For example, one of the simplest is the half adder, which finds the sum of two bits Binary addition). It outputs a sum and a carry. That's a part of the truth table.
For the Half Adder, sum is simply an XOR and the carry is just an AND! Really cool. Just two boolean functions!
A full adder allows us to process the carry in bit. We get sum and carry out as the output. This gives us a full adder!
In fact, combine half adders to make a full one! Full adders can be connected in a series. The carry bit 'ripples' from one ader to the next; hence, this configuration is called a ripple-carry adder.
Decoder
Is another important type of combinational circuit.
(There are some errors in the book btw. He states some of the circuits may be off such as with the 2-to-4 decoder).
Multiplexer
Opposite of a decoder. Selects a single output from serveral inputs. The particular input chosen for output is determined by the value of the multiplexer's control lines.
