Number System
Number Systems
Base 2: The Binary Number System
Base 8: The Octal Number System
Base 16: The Hexadecimal Number System
Learning Objectives
• At the end of the lesson the student should be able to:
– Identify the different number base system
– Convert base ten numbers to base two, eight or sixteen
– Convert base two, eight or sixteen numbers to base ten
– Perform basic operations on various base numbers
Number Base
• What is a number base?
A number base is a specific collection of symbols on which a number system can be built.
• The number base familiar to us is base 10, upon which the decimal number system is built. There are ten symbols - 0 to 9 - used in thesystem.
Place Value
• What is the concept of place value?
Place value means that the value of a digit in a number depends not only on its own natural value but also on its location in the number. It is used interchangeably with the term positional notation.
• Place value tells us that the two 4s in the number 3474 have different values, that is, 400 and 4, respectively.
A Review of the Decimal Number System
• The word “decimal” comes from the Latin word decem, meaning ten.
• Thus, the number base of the decimal number system is base 10.
• Since it is in base 10, ten symbols are used in the decimal number system. {0,1,2,3,4,5,6,7,8,9}
• This means that only the digits in the above set can be used for each position in every place value in a given decimal number.
A Review of the Decimal Number System
2 7 0
• Note that the highlighted place value can be filled by the digits in the set {0,1,2,3,4,5,6,7,8,9}.
• Thus, it can be increased by 1 until it reaches -
2 7 9
• At this point, the symbols that can be used to fill the highlighted position has been exhausted. Increasing it further causes a shift in place value, and resets the initial place value to zero. Thus -
2 8 0
A Review of the Decimal Number System
Base 2: The Binary Number System
Base 8: The Octal Number System
Base 16: The Hexadecimal Number System
Learning Objectives
• At the end of the lesson the student should be able to:
– Identify the different number base system
– Convert base ten numbers to base two, eight or sixteen
– Convert base two, eight or sixteen numbers to base ten
– Perform basic operations on various base numbers
Number Base
• What is a number base?
A number base is a specific collection of symbols on which a number system can be built.
• The number base familiar to us is base 10, upon which the decimal number system is built. There are ten symbols - 0 to 9 - used in thesystem.
Place Value
• What is the concept of place value?
Place value means that the value of a digit in a number depends not only on its own natural value but also on its location in the number. It is used interchangeably with the term positional notation.
• Place value tells us that the two 4s in the number 3474 have different values, that is, 400 and 4, respectively.
A Review of the Decimal Number System
• The word “decimal” comes from the Latin word decem, meaning ten.
• Thus, the number base of the decimal number system is base 10.
• Since it is in base 10, ten symbols are used in the decimal number system. {0,1,2,3,4,5,6,7,8,9}
• This means that only the digits in the above set can be used for each position in every place value in a given decimal number.
A Review of the Decimal Number System
2 7 0
• Note that the highlighted place value can be filled by the digits in the set {0,1,2,3,4,5,6,7,8,9}.
• Thus, it can be increased by 1 until it reaches -
2 7 9
• At this point, the symbols that can be used to fill the highlighted position has been exhausted. Increasing it further causes a shift in place value, and resets the initial place value to zero. Thus -
2 8 0
A Review of the Decimal Number System