24 Questions
What is the base of the binary number system?
2
Which method can be used to convert a decimal number to a binary number?
Division method
What are the column weights of binary numbers for fractional parts?
$2^{-2}, 2^{-3}, 2^{-4}$
How can a decimal whole number be converted to binary using the subtraction method?
By subtracting powers of 2 from the decimal number
What is the result when an even number is divided by 2?
Remainder is 0
How can a decimal number be converted to binary?
By repeatedly dividing by 2
What is the purpose of using hexadecimal to represent binary values?
To reduce the number of digits required
What are the column weights in the hexadecimal number system?
Powers of 16
How can a binary number be converted to octal?
By grouping bits 4 at a time and writing the equivalent octal character
What are the characters used in the octal number system?
0-7
What is the result when an odd number is divided by 2?
Remainder is 1
What is the base of the octal number system?
8
What are the column weights for fractional parts in the octal number system?
Negative powers of eight that decrease from left to right
What is the result when an odd number is divided by 2 in the binary system?
The quotient is even
How can a binary number be converted to hexadecimal?
Grouping the binary number in sets of four bits and replacing each set with its corresponding hexadecimal digit
What is the base of the hexadecimal number system?
16
What is the result when an even number is divided by 2 in the octal system?
The quotient is even
What is the purpose of using octal to represent binary values?
To reduce the number of required bits for storage
How can a decimal whole number be converted to binary using the division method?
Dividing the number by 2 and recording the remainders in reverse order
What are the characters used in the binary number system?
0, 1
What is the base of the binary number system?
2
What is the result when a binary number is divided by 2?
The quotient is even
What are the column weights for fractional parts in the hexadecimal number system?
Negative powers of sixteen that increase from right to left
What is the result when an odd number is divided by 2 in the octal system?
The quotient is odd
Study Notes
Number Systems
- The base of the binary number system is 2.
- The binary system uses characters 0 and 1.
Binary Conversions
- A decimal number can be converted to binary using the subtraction method or the division method.
- The division method involves repeatedly dividing the decimal number by 2 and recording the remainders.
Hexadecimal Number System
- The purpose of using hexadecimal is to represent binary values in a more compact form.
- The base of the hexadecimal number system is 16.
- The column weights in the hexadecimal number system are 16^0, 16^1, 16^2, ... .
- The column weights for fractional parts in the hexadecimal number system are 16^(-1), 16^(-2), 16^(-3), ... .
- A binary number can be converted to hexadecimal by dividing it into groups of 4 bits and replacing each group with the corresponding hexadecimal digit.
Octal Number System
- The purpose of using octal is to represent binary values in a more compact form.
- The base of the octal number system is 8.
- The column weights in the octal number system are 8^0, 8^1, 8^2, ... .
- The column weights for fractional parts in the octal number system are 8^(-1), 8^(-2), 8^(-3), ... .
- The characters used in the octal number system are 0, 1, 2, 3, 4, 5, 6, and 7.
- A binary number can be converted to octal by dividing it into groups of 3 bits and replacing each group with the corresponding octal digit.
Properties of Divisions
- When an even number is divided by 2, the result is an integer.
- When an odd number is divided by 2, the result is a decimal with a fractional part of 0.5.
Test your understanding of decimal number systems and conversion methods with this quiz. Evaluate your knowledge of column weights, radix, and the representation of numbers using only ten symbols.
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