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Questions and Answers
What is the capacity of a terabyte in bytes?
In hexadecimal, what does the letter 'C' represent?
In binary multiplication, what is the result of 1 multiplied by 0?
How is base-r to decimal conversion done?
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How is the range of coefficients for multiplication different from the usual when converting decimal numbers to octal?
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How is the conversion of decimal numbers with both integer and fraction parts done?
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What is the correspondence between octal and binary digits?
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How is the conversion from binary to hexadecimal different from the conversion to octal?
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In binary numbers, when does a change from 0111 to 1000 produce an intermediate erroneous number?
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What is the purpose of Gray code in the context of optical shaft encoders?
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How many elements does an alphanumeric character set typically contain?
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Which bit in ASCII code is designated as the most significant bit?
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Study Notes
Data Conversion Basics
- One terabyte (TB) equals 1,000,000,000,000 bytes or 10^12 bytes in the decimal system.
- In hexadecimal, the letter 'C' represents the decimal value of 12.
Binary Operations and Concepts
- In binary multiplication, any number multiplied by 0 results in 0; therefore, 1 multiplied by 0 equals 0.
- A conversion from base-r to decimal involves multiplying each digit by r raised to its positional exponent and summing the results.
Octal and Decimal Conversions
- When converting decimal numbers to octal, the range of coefficients (or digits) is limited to 0-7, unlike the usual 0-9 in decimal.
- Decimal to octal conversion can handle both integer and fractional parts by converting the integer part using repeated division and the fractional part using multiplication by 8.
Octal and Binary Correspondence
- Each octal digit corresponds to a unique set of three binary digits, making conversion straightforward by grouping binary bits into groups of three.
Binary to Hexadecimal Conversion
- Converting from binary to hexadecimal requires grouping binary digits into sets of four, differing from octal's groups of three. Each hexadecimal digit represents four binary bits.
Binary Transition and Errors
- In binary, transitioning from 0111 (7 in decimal) to 1000 (8 in decimal) results in an erroneous intermediate number, specifically if considerate of carry operations in addition leading to overflow.
Gray Code
- Gray code is used in optical shaft encoders to minimize errors during the transition between states, as only one bit changes at a time, reducing the likelihood of misreading.
Character Sets and ASCII
- An alphanumeric character set typically contains 62 elements, representing uppercase, lowercase letters, and digits.
- In ASCII code, the most significant bit (MSB) is the leftmost bit, used for extended character sets and indicating control characters.
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Description
Test your understanding of converting decimal fraction numbers to octal numbers. Practice converting numbers with both integer and fraction parts separately and then combining the two results.
