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.

The choice of character set significantly impacts the size of data stored in a file. Character sets with fewer bits per character (like ASCII) require less storage space than character sets with more bits per character (like Unicode). This is because each character is represented by a different number of bytes.

Example: Consider the string "Hello".

ASCII Encoding: Each character in "Hello" can be represented using 7 bits. Therefore, the string requires 5 characters * 7 bits/character = 35 bits. Since bits are typically stored in bytes (8 bits), this translates to 35 bits / 8 bits/byte = 4.375 bytes. In practice, this would be rounded up to 5 bytes.

UTF-8 Encoding: UTF-8 is a variable-length encoding. ASCII characters (like 'H', 'e', 'l', 'o') are represented by a single byte. However, some characters (e.g., accented characters like 'é') require multiple bytes. In the case of "Hello", each character is represented by a single byte, so the string requires 5 bytes.

UTF-16 Encoding: UTF-16 uses 2 bytes per character. Therefore, "Hello" would require 5 characters * 2 bytes/character = 10 bytes.

This example demonstrates that using a more compact character set like ASCII can reduce the storage space required for text data, while using a more comprehensive character set like UTF-16 can increase the storage space. The choice depends on the requirements of the application, considering factors like the range of characters that need to be supported and the available storage space.

Binary to Decimal Conversion:

Decimal equivalent: 1 + 0*2 + 1*4 + 1*8 + 0*16 + 1*32 + 0*64 + 1*128 = 1 + 0 + 4 + 8 + 0 + 32 + 0 + 128 = 173

Decimal to Hexadecimal Conversion:

173 divided by 16 is 10 with a remainder of 13. 13 is D in hexadecimal.

Therefore, the hexadecimal equivalent is D9.