1.Describe the term digital
2.what is meant by decimal number system
3.state De Morgan's first theorem
4.state the function of the decoder
5.Define commutative law
1. The term digital refers to anything that involves or relates to the use of digits or numerical representation. It specifically refers to data or information that is in a digital format, which means it is represented using discrete values or units, typically in the form of binary code (0s and 1s).
2. The decimal number system, also known as the base-10 system, is a numerical system that uses ten symbols (0-9) to represent numbers. It is the most widely used number system in daily life. Each digit in a decimal number has a position value based on powers of 10. For example, the number 235 in decimal means: 2 x 10^2 + 3 x 10^1 + 5 x 10^0 = 200 + 30 + 5.
3. De Morgan's First Theorem states that the complement of the union of two sets is equal to the intersection of their complements. In simple terms, it states that the negation of the OR operation between two events is equivalent to the AND operation of their negations. Symbolically, it can be written as: (A U B)' = A' ∩ B'.
4. The function of a decoder is to convert a coded input into its corresponding output. It is typically used in digital systems and circuits to decode binary-encoded data into a format that can be understood or processed by other components. Decoders are commonly used in applications such as demultiplexing, address decoding, and data routing.
5. The commutative law, also known as the commutative property, states that the order of the operands does not affect the result of a binary operation. In the context of mathematics, it refers to the ability to change the order of addition or multiplication without changing the outcome. For example, the commutative law of addition states that a + b is equal to b + a, and the commutative law of multiplication states that a x b is equal to b x a.