Truth Tables
This type of table lists all possible input combinations and their corresponding outputs for a logic circuit.
What is a truth table?
This type of logic circuit produces outputs based only on the current inputs, without memory of past states.
What is a combinational logic circuit?
This type of logic expression combines ANDed terms using OR gates to form a complete circuit.
What is a Sum-of-Products (SOP) expression
This 19th-century mathematician developed the algebraic system used to simplify logic circuits.
Who is George Boole
This mathematician, born in India in 1806, is best known for the logic theorems that simplify Boolean expressions
Who is Augustus DeMorgan
A logic design with N inputs will have this many input combinations.
What is 2N
When analyzing a circuit, the first step is to determine this table and the corresponding logic expression for the output.
What is the truth table?
When designing an SOP circuit, each minterm is implemented using this type of gate.
What is an AND gate
This law states that the order of variables does not affect the result in AND or OR operations
What is the Commutative Law
DeMorgan’s first theorem states that the complement of an AND operation equals this type of operation on the complemented variables
What is an OR operation
o write a Sum-of-Products (SOP) expression from a truth table, you sum together these terms for every row where the output is 1.
What are minterms?
In the procedure “Circuit to Truth Table to Logic Expression,” these are added at the output of every gate to help complete the truth table.
What are test points?
If you only have 2-input OR gates and 3-input AND gates, what technique must you use to implement larger logic expressions?
What is cascading gates
According to Boolean Theorem #4, the expression X+0 simplifies to this
What is X
DeMorgan’s second theorem states that the complement of an OR operation equals this type of operation on the complemented variables
What is an AND operation
A fuel tank alarm system uses two sensors: pressure and temperature. Both output LOW when safe. The alarm sounds if either sensor is unsafe. What is the logic expression for the alarm?
What is A=P+T
After completing a truth table, you identify these terms from rows where the output is 1 to write the Sum-of-Products expression.
What are minterms
In a Product-of-Sums (POS) circuit, each maxterm is implemented using this type of gate before combining them with AND gates.
What is an OR gate
This theorem allows you to eliminate redundant terms like XY+X′Z+YZ by removing the last term
What is the Consensus Theorem
When applying DeMorgan’s Theorems, this phrase reminds you to invert the operation when breaking a complement line over variables
What is “Break the line, change the sign”
Given the SOP expression F=A'B+CD, how many rows in the truth table will have an output of 1?
What is 6 rows?
If a circuit has three inputs (X, Y, Z) and the output is 1 for input combinations 011, 100, and 101, what is the SOP expression for the output?
What is F=X'YZ+XY'Z'+XY'Z
For the SOP expression F=AB+CD+BD, how many AND gates and OR gates are required to implement the circuit using only 2-input gates?
What are 3 AND gates and 2 OR gates
Simplify the Boolean expression AB'+AB+AB'C using Boolean algebra
What is A
Simplify the expression (X+Y)'⋅(Y+Z)' using DeMorgan’s Theorems
What is X'⋅Y'⋅Y'⋅Z', which simplifies to X'⋅Y'⋅Z'