Mathematical laws and theorems- Describe and Discuss:
- Associative Law, Distributive Law, and Commutative Law
- Associative law is a mathematical principle that states that the grouping or association of three numbers does not affect the result of addition or multiplication, It can be expressed symbolically as a + (b + c) = (a + b) + c and a(bc) = (ab)c for any variables a, b, and c. Associative law does not apply to subtraction, division, or some other applications like non associative algebras.
- Distributive law is a type of algebraic law that relates the operations of multiplication and addition. It says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. 3 × (2 + 4) = 3×2 + 3×4.
- Commutative law is a rule in mathematics that relates to number operations of addition and multiplication. It states that when we add or multiply two numbers, the final value remains the same, even if we change the position of the two numbers. a + b = b + a.
- Associative Law, Distributive Law, and Commutative Law
The Commutative, Associative and Distributive Laws – YouTube
- De Morgan’s Theorem
- Demorgan’s theorem establishes the uniformity of a gate with identically inverted input and output. It is used to implement fundamental gate functions like the NAND gate and NOR gate. De Morgan’s theorems are used to answer Boolean algebraic expressions. It is an extremely effective tool for digital design.
De Morgan’s Theorem | Understand circuit simplification | Boolean algebra basics – YouTube
- Karnaugh Mapping
- Maurice Karnaugh, a telecommunications engineer, developed the Karnaugh map at Bell Labs in 1953 while designing digital logic based telephone switching circuits. The Karnaugh map is used to help find the next output.
References:
De Morgan’s Theorems : Introduction, Proof, Applications and Examples. (testbook.com)
- Mathematical laws and theorems- Describe and Discuss:
- Associative Law, Distributive Law, and Commutative Law
- Associative law is a mathematical principle that states that the grouping or association of three numbers does not affect the result of addition or multiplication, It can be expressed symbolically as a + (b + c) = (a + b) + c and a(bc) = (ab)c for any variables a, b, and c. Associative law does not apply to subtraction, division, or some other applications like non associative algebras.
- Distributive law is a type of algebraic law that relates the operations of multiplication and addition. It says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. 3 × (2 + 4) = 3×2 + 3×4.
- Commutative law is a rule in mathematics that relates to number operations of addition and multiplication. It states that when we add or multiply two numbers, the final value remains the same, even if we change the position of the two numbers. a + b = b + a.
- Associative Law, Distributive Law, and Commutative Law
The Commutative, Associative and Distributive Laws – YouTube
- De Morgan’s Theorem
- Demorgan’s theorem establishes the uniformity of a gate with identically inverted input and output. It is used to implement fundamental gate functions like the NAND gate and NOR gate. De Morgan’s theorems are used to answer Boolean algebraic expressions. It is an extremely effective tool for digital design.
De Morgan’s Theorem | Understand circuit simplification | Boolean algebra basics – YouTube
- Karnaugh Mapping
- Maurice Karnaugh, a telecommunications engineer, developed the Karnaugh map at Bell Labs in 1953 while designing digital logic based telephone switching circuits. The Karnaugh map is used to help find the next output.
References:
De Morgan’s Theorems : Introduction, Proof, Applications and Examples. (testbook.com)
