A notational system is a way of writing numbers using symbols or digits. The base or radix of a notational system is the number of symbols or digits it uses to represent numbers. For example, the decimal system uses 10 symbols (0 to 9) and has a base of 10. The octal system uses 8 symbols (0 to 7) and has a base of 8. The hexadecimal system uses 16 symbols (0 to 9 and A to F) and has a base of 16. The binary system uses 2 symbols (0 and 1) and has a base of 2.
To represent the decimal number 10 in different notational systems, we need to convert it to the corresponding base. This can be done by dividing the number by the base repeatedly and writing the remainders in reverse order. For example:
To convert 10 to octal, we divide 10 by 8 and get a quotient of 1 and a remainder of 2. Then we divide 1 by 8 and get a quotient of 0 and a remainder of 1. The remainders in reverse order are 12, so 10 in octal is 12.
To convert 10 to hexadecimal, we divide 10 by 16 and get a quotient of 0 and a remainder of 10. The remainder is 10, which is represented by the symbol A in hexadecimal, so 10 in hexadecimal is A.
To convert 10 to binary, we divide 10 by 2 and get a quotient of 5 and a remainder of 0. Then we divide 5 by 2 and get a quotient of 2 and a remainder of 1. Then we divide 2 by 2 and get a quotient of 1 and a remainder of 0. Then we divide 1 by 2 and get a quotient of 0 and a remainder of 1. The remainders in reverse order are 1010, so 10 in binary is 1010.
The notational system that uses the most characters to represent the decimal number 10 is the binary system, which uses 4 characters (1010). The octal system uses 2 characters (12), the hexadecimal system uses 1 character (A), and the decimal system uses 2 characters (10).
References: CompTIA IT Fundamentals (ITF+) Certification Guide, pages 216-217. Numeral Systems: Binary, Decimal, Conversion | StudySmarter.
