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Questions and Answers
What is the base of the binary number system?
What is the term used to describe each digit in the hexadecimal number system?
How many bits are used to represent each decimal digit in the binary number system?
What is the purpose of the octal number system?
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How do you convert a binary number to a decimal number?
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What is the term used to describe a group of 3 bits in the octal number system?
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How do you convert a hexadecimal number to a binary number?
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What is the term used to describe a group of 4 bits in the binary number system?
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How do you convert a decimal number to a binary number?
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Study Notes
Number System in Computers
Binary Number System
- Uses only two digits: 0 and 1
- Base-2 number system
- Each digit is called a bit
- 8-bit binary number is called a byte
- Used by computers for internal representation of data
- Conversion: Each decimal digit can be represented by a 4-digit binary number (0000 to 1001)
Hexadecimal Number System
- Uses 16 digits: 0-9 and A-F (A=10, B=11, ..., F=15)
- Base-16 number system
- Each digit is called a nibble (4-bit binary number)
- Often used in programming and coding due to its human-readable format
- Conversion: Each hexadecimal digit can be represented by a 4-digit binary number (0000 to 1111)
Octal Number System
- Uses 8 digits: 0-7
- Base-8 number system
- Less commonly used than binary and hexadecimal
- Often used in Unix file permissions and some programming languages
- Conversion: Each octal digit can be represented by a 3-digit binary number (000 to 111)
Number System Conversion
- Binary to Decimal: Convert each binary digit to decimal (0 or 1) and sum the powers of 2
- Binary to Hexadecimal: Divide the binary number into groups of 4 bits (nibbles) and convert each group to hexadecimal
- Binary to Octal: Divide the binary number into groups of 3 bits and convert each group to octal
- Decimal to Binary: Convert each decimal digit to a 4-digit binary number
- Hexadecimal to Binary: Convert each hexadecimal digit to a 4-digit binary number
- Octal to Binary: Convert each octal digit to a 3-digit binary number
Number Systems in Computers
Binary Number System
- Uses only two digits: 0 and 1, making it a base-2 number system
- Each digit is called a bit, and 8 bits make up a byte
- Computers use binary internally to represent data
- Each decimal digit can be represented by a 4-digit binary number (0000 to 1001)
Hexadecimal Number System
- Uses 16 digits: 0-9 and A-F (A=10, B=11,..., F=15), making it a base-16 number system
- Each digit is called a nibble, which is a 4-bit binary number
- Hexadecimal is often used in programming and coding due to its human-readable format
- Each hexadecimal digit can be represented by a 4-digit binary number (0000 to 1111)
Octal Number System
- Uses 8 digits: 0-7, making it a base-8 number system
- Often used in Unix file permissions and some programming languages
- Each octal digit can be represented by a 3-digit binary number (000 to 111)
Number System Conversions
- Binary to Decimal: Convert each binary digit to decimal (0 or 1) and sum the powers of 2
- Binary to Hexadecimal: Divide the binary number into groups of 4 bits (nibbles) and convert each group to hexadecimal
- Binary to Octal: Divide the binary number into groups of 3 bits and convert each group to octal
- Decimal to Binary: Convert each decimal digit to a 4-digit binary number
- Hexadecimal to Binary: Convert each hexadecimal digit to a 4-digit binary number
- Octal to Binary: Convert each octal digit to a 3-digit binary number
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Description
A quiz on the basics of number systems used in computers, covering binary and hexadecimal systems, their representations, and conversions.