2 Digital Logic Free Online FlashCards

What does Boolean algebra describe?

Boolean algebra describes variables that take one of two values, 0 or 1, and expressions that determine outputs from those values.

When does AND output 1?

AND outputs 1 only when both inputs are 1; its Boolean expression is $A \cdot B$, or simply $AB$.

When does inclusive OR output 1?

OR outputs 1 when at least one input is 1, including when both inputs are 1; it is written $A+B$.

When does XOR output 1?

XOR outputs 1 when its inputs differ and 0 when they match; it is written $A \oplus B$.

When does XNOR output 1?

XNOR outputs 1 when its inputs match and 0 when they differ; it is the complement of XOR.

How are NAND and NOR related to AND and OR?

NAND is the complement of AND, $\neg(A \cdot B)$; NOR is the complement of OR, $\neg(A+B)$.

How many input combinations are there for $n$ binary inputs?

A truth table has $2^n$ input combinations for $n$ binary inputs.

What are the Boolean identity rules for OR with 0 and AND with 1?

The identity rules are $A+0=A$ and $A \cdot 1=A$: OR with 0 and AND with 1 leave $A$ unchanged.

What happens when a Boolean value is ORed or ANDed with itself?

The idempotent rules are $A+A=A$ and $A \cdot A=A$.

What are the Boolean complement rules?

A value ORed with its complement is 1, while a value ANDed with its complement is 0: $A+A'=1$ and $A \cdot A'=0$.

What do De Morgan’s laws say?

De Morgan’s laws are $\neg(A \cdot B)=\neg A+\neg B$ and $\neg(A+B)=\neg A \cdot \neg B$.

What determines a combinational circuit’s outputs?

A combinational circuit’s outputs depend only on its current inputs, not on earlier inputs or stored state.