Understanding Subscripts: Converting Decimal to Binary and Binary to Decimal
Why are subscripts are used to convert decimal to binary and binary to decimal?
Answer:
Subscripts are used to convert decimal to binary and binary to decimal because they help in clearly representing the base of the number system being used. In the context of conversion between decimal and binary systems, subscripts are crucial in indicating the base of the numbers involved.
Decimal Number System
The decimal number system is the most commonly used system, known as Base 10, which is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In the decimal system, each digit has its own position along with the decimal point. For example, the number 356.74 has digits positioned at Hundredths, Tenths, Units, Tens, and Hundreds. The decimal system is one of the oldest numeral systems and is historically related to the Hindu-Arabic numeral system.
Binary System
The binary system is the simplest number system, using only two digits 0 and 1. This system is widely used in digital electronics as transistors operate in two states that can be represented by 0 and 1. The binary system is preferred in modern computer engineering, networking, communication specialties, and other professional fields.
Decimal to Binary Conversion Examples
Some examples of decimal to binary conversions are:
(51)10 = (110011)2
(217)10 = (11011001)2
(8023)10 = (1111101010111)2
Using subscripts in these conversions helps in distinguishing between the base 10 (decimal) and base 2 (binary) number systems, making the representation clear and accurate.