22 Questions
What is the base of the decimal system?
10
What is the base of the decimal system?
10
What is positional notation?
A system in which the value of a number is defined by both the symbol and its position
What is positional notation?
A system in which the value of a number is defined not only by the symbol but by the symbol’s position
What is the base of the binary numbering system?
2
What is the base of the binary numbering system?
2
What is the octal numbering system?
A system in which each octal numeral can be represented by three binary digits
What is the importance of using zero in a number?
It can affect the value being represented
What is the base of the octal numbering system?
8
What is the hexadecimal numbering system?
A system in which each hexadecimal digit represents four binary digits
What is Binary Coded Decimal (BCD)?
A system that combines some characteristics of binary and decimal number systems
How many binary digits does each octal digit represent?
Three
What is the base of the hexadecimal numbering system?
16
How can BCD numbers be easily converted to decimal?
By breaking them into 4-bit groups and converting them to decimal
How many binary digits does each hexadecimal digit represent?
Four
How can you convert binary to decimal?
By using the binary truth table
How can you convert octal to decimal?
By multiplying each octal digit by its corresponding power of 8 and adding them up
What is Binary Coded Decimal (BCD)?
A compromise code that combines some characteristics of binary and decimal number systems
What is the universal method of counting and recording values?
Decimal system
How can BCD numbers be easily converted to decimal?
By breaking them into 4-bit groups and converting them to decimal
What is the universal method of counting and recording values?
Decimal system
How can octal be converted to decimal?
By multiplying each octal digit by its corresponding power of 8 and adding them up
Study Notes
- Numbering systems have units, numbers, and bases.
- The base of a numbering system tells you the number of symbols used in that system.
- The base of the decimal system is 10, while other systems may have different bases.
- Positional notation is a system in which the value of a number is defined not only by the symbol but by the symbol’s position.
- The use of zero is important in a number as it can affect the value being represented.
- The binary numbering system is the base 2 numbering system, using only 0 and 1 as symbols.
- A computer works only in digital, using zeros and ones.
- The decimal system is the universal method of counting and recording values.
- The octal system is widely used in computer application sectors and digital numbering systems.
- Each octal numeral can be represented by three binary digits.
- The octal numbering system has a base of 8 and uses numerals 0-7.
- Each octal digit represents three binary digits.
- The hexadecimal numbering system has a base of 16 and uses numerals 0-9 and A-F.
- Each hexadecimal digit represents four binary digits.
- Binary Coded Decimal (BCD) is a compromise code that combines some characteristics of binary and decimal number systems.
- BCD numbers can be easily converted to decimal by breaking them into 4-bit groups and converting them to decimal.
- Converting from binary to decimal involves using the binary truth table or repeatedly dividing the decimal number by 2 and recording the remainder digits.
- Decimal to binary conversion can be done using either division or subtraction methods.
- Octal to decimal conversion involves multiplying each octal digit by its corresponding power of 8 and adding them up.
- Decimal to octal conversion involves repeatedly dividing the decimal number by 8 and recording the remainder digits.
- There are different numbering systems, including binary, octal, decimal, and hexadecimal.
- Converting between these systems can be done using truth tables and division methods.
- To convert decimal to binary, divide by 2 and record the remainders.
- To convert binary to decimal, use the binary to decimal truth table.
- To convert octal to binary, use the octal truth table, then convert to decimal using the binary to decimal truth table.
- To convert decimal to octal, divide by 8 and record the remainders.
- Hexadecimal can be converted to binary and then to decimal using the binary to decimal truth table.
- To convert decimal to hexadecimal, divide by 16 and represent remainders higher than 9 with the appropriate letter.
- Converting to and from binary can simplify conversions between different numbering systems.
- Practice exercises are provided to reinforce understanding of conversions.
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