1.4.3 Boolean Algebra Flashcards
What are the 6 primary types of logic gates?
AND
OR
NOT
XOR
NAND
NOR
What is the name, gate diagram, symbol, and explanation for an AND gate?
- Conjunction
- Ʌ
- Only produces a True output if both inputs are True
![](https://s3.amazonaws.com/brainscape-prod/system/cm/320/381/687/a_image_thumb.png?1599600739)
What is the name, gate diagram, symbol, and explanation for an OR gate?
- Disjunction
- V
- It is True when any one input is True
![](https://s3.amazonaws.com/brainscape-prod/system/cm/320/381/864/a_image_thumb.png?1599600818)
What is the name, gate diagram, symbol, and explanation for a NOT gate?
- Negation
- ¬
- It flips a value to its opposite
![](https://s3.amazonaws.com/brainscape-prod/system/cm/320/381/916/a_image_thumb.png?1599600873)
What is the name, gate diagram, symbol, and explanation for an XOR gate?
- Exclusive Disjunction
- V
- True when any one input is True, but not when both are True
![](https://s3.amazonaws.com/brainscape-prod/system/cm/320/381/988/a_image_thumb.png?1599600955)
Describe De Morgan’s Law
This states the relationship between AND and OR operators
A ∧ B = ¬(¬A ∨ ¬B)
A ∨ B = ¬(¬A ∧ ¬B)
Describe the Distribution law
This law is equivalent to factorising or expanding brackets
X ∨ (Y ∧ Z) = (X ∨ Y) ∧ (X ∨ Z)
Describe the Association law
This law states that when using multiple operations of the same type, the operand order doesn’t matter
X ∧ (Y ∧ X) = (X ∧ Y) ∧ X
Describe the Commutation law
This law states it doesn’t matter which side of an AND or OR gate the operands are on
X ∧ Y = Y ∧ X
Describe the Double negation law
This law states a double NOT cancels itself out
¬(¬X) = X
Describe the Absorption law
This law states that something ORed/ANDed with the AND/OR of itself and another is equal to the original
X ∨ (X ∧ Y) = X
Describe a half adder
A group of logic gates used to add numbers
What is a half adder used for?
Taking 2 single-bit numbers and adding them together, producing a digit bit and a carry bit
What does the logic circuit of a half adder look like?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/320/450/518/a_image_thumb.png?1599652712)
Describe a full adder
A system of logic gates used to add 2 numbers together