Logic Networks … and the card game Boolette. MAT 385 Mullins - Reinecke. Overview. Logic networks, or digital circuits, are physical elements used in computers to perform arithmetic operations or make logical choices.
MAT 385 Mullins - Reinecke
Logic gates are the building blocks that make up digital circuits.
A gate receives one or more inputs (binary 1s and 0s), performs a Boolean operation on them, and outputs the result as a 1 or 0.
The logic gates shown to the left represent their Boolean algebra counterparts: * for AND, + for OR, ‘ for NOT. The NAND and NOR gates are simply the negation (‘) of AND and OR expressions. The NOT gate, also called an inverter, represents the negation of a single input. XOR outputs a 1 only when inputs differ.
Our inputs are x1 and x2, and F represents the function of the two inputs. We focus on where the output of the function is a 1, so there are three products to sum.
As a Boolean algebraic expression, the SOP would look like this:
x1x2 + x1x2’ + x1’x2’
This expression can be used to create the following logic network:
S: 1 XOR 1 = 0
C: 1 AND 1 = 1
Note: The sum only shows the last bit. The real answer to this would be S=10, C=1 but we can only store one digit for S.
S: 1 XOR 0 = 1, 1 XOR 1 = 0
Cout: 1 XOR 0 = 1, 1 AND 1 = 1, 1 AND 0 = 0,
1 OR 0 = 1
Ex: Arithmetic right shift of 1011 will be 1101.
The 4-bit right shifter takes a selector bit and 4 input bits, producing an output of 4 bits.
AND 0, AND 1,
OR 0, OR 1,
XOR 0, XOR 1,
giving a total of 28 cards.
The NOT card has wiped out cards from both players’ pyramids. While both players must begin to rebuild, player 2 now has more valid cards than player 1.
Notice in the first image that player 1 was only one card away from victory when player 2 played a NOT card.