Computer Science – 1.1 Data Representation | e-Consult
1.1 Data Representation (1 questions)
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Let's analyze the storage requirements for storing an 8-bit integer (0-255) using binary, decimal, and hexadecimal representations:
- Binary: An 8-bit integer requires 8 bits of storage. The range 0-255 can be represented with 8 bits, so each integer needs 8 bits.
- Decimal: Decimal representation uses base-10. To represent each integer, we would need to store the decimal value directly. The number of digits required depends on the value of the integer. For example, 0-9 require one digit, 10-99 require two digits, and so on. The storage required is variable and depends on the range of values.
- Hexadecimal: Hexadecimal representation uses base-16. Each hexadecimal digit represents 4 bits. Therefore, to represent an 8-bit integer, we need 2 hexadecimal digits (8 bits / 4 bits per hex digit = 2 hex digits). The range 0-255 can be represented with 2 hexadecimal digits (00-FF).
Comparison:
Binary: 8 bits
Decimal: Variable (depends on the value)
Hexadecimal: 2 digits (representing 8 bits)
Efficiency: Hexadecimal is the most efficient representation in terms of storage space. It requires only 2 digits to represent an 8-bit integer, whereas binary requires 8 bits and decimal requires a variable number of digits. This makes hexadecimal a popular choice for representing binary data in a compact and human-readable format, especially in areas like memory addressing and data encoding.