Subjects number systems

Hex Decimal Binary

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Hex Decimal Binary


1. The problem involves understanding the relationship between hexadecimal, decimal, and binary numbers as shown in the table. 2. Hexadecimal (base 16) numbers use digits 0-9 and letters a-f to represent values 0 to 15. 3. Decimal (base 10) numbers use digits 0-9. 4. Binary (base 2) numbers use digits 0 and 1. 5. Each hexadecimal digit corresponds to exactly 4 binary digits (bits). 6. For example, the hex number \texttt{1} corresponds to decimal 1 and binary \texttt{1}. 7. The hex number \texttt{4c} corresponds to decimal 76 and binary \texttt{7f} (127 in decimal). 8. The table shows increasing values in hex, decimal, and binary, illustrating how these number systems relate. 9. To convert hex to decimal, multiply each digit by 16 raised to the power of its position index (from right to left, starting at 0) and sum. 10. To convert hex to binary, replace each hex digit with its 4-bit binary equivalent. 11. The last column appears to be a decimal fraction or probability associated with each row. 12. Understanding these conversions is fundamental in computer science and digital electronics. Final answer: The table demonstrates the conversion and relationship between hexadecimal, decimal, and binary numbers, with an additional decimal fraction column.