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WEEK 7
TOPIC: OVERVIEW OF NUMBER BASES
CONTENT:
- Review of number bases
- Conversion in Number bases
- Basic Arithmetic in number bases
SUBTOPIC 1: REVIEW OF NUMBER BASES
Most computer systems operate using binary logic. The binary number system works like the decimal number system except that the binary number systems use base 2, and its digits are 0 and 1 while decimal system uses base 10 and its digits are from 0 – 9.
The common number systems used in computing are:
- Base 10 known as Decimal Number System
- Base 2 known as Binary Number System
- Base 8 known as Octal Number System
- Base 16 known as Hexadecimal Number System
Binary Number system:
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1.
Octal Number System:
The octal numeral system is the base 8 number system, and uses the digits 0-7. Numerals can be made from binary numerals by grouping consecutive binary digits into group of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010. Therefore, the octal representation is 112.
Decimal Number System:
the decimal numeral system (also called base ten or occasionally denary) has ten as its base. It is the most common notation and often refers to a base-10 positional notation.
Hexadecimal Number System:
Hexadecimal (also base 16, or hex) is a positional numeral system with a base of 16, i.e. it uses sixteen distinct symbols, i.e. 0-9, A-F representing values 10-15.
SUBTOPIC 2: CONVERSION IN NUMBER BASES
From Decimal to other bases:
To convert from base 10 to any other base, simply divide the given number continuously by the number base being converted to, until its no longer divisible. Then the remainders are copied in ascending order.
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