First, we need to convert the binary number 01001000 to decimal. This can be done as follows:

Adding these values together: 0 + 1 + 2 + 4 + 8 + 16 + 32 = 63

Since the encoding is 7-bit, the value 63 represents the character 'C' in the ASCII table. Therefore, the character represented by the binary number 01001000 is 'C'.

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.

Unsigned Binary Numbers: Unsigned binary numbers represent only non-negative integers. They use all the bits to represent the magnitude of the number. For example, an 8-bit unsigned binary number can represent values from 0 to 255.

Signed Binary Numbers: Signed binary numbers represent both positive and negative integers. There are several methods for representing signed numbers, the most common being two's complement.

Two's Complement Representation: In two's complement, the most significant bit (MSB) represents the sign: 0 for positive, 1 for negative. To represent a negative number, you find the binary representation of its absolute value, then invert all the bits (1s become 0s and 0s become 1s), and finally add 1 to the result.

Example: Let's represent the decimal number -5 using an 8-bit two's complement system.

1. Binary representation of 5: 00000101
2. Invert the bits: 11111010
3. Add 1: 11111010 + 1 = 11111011

Therefore, the two's complement representation of -5 is 11111011.

Why Two's Complement is Used:

• Simplified Arithmetic: Two's complement allows computers to perform addition and subtraction using the same circuitry for both positive and negative numbers. This simplifies hardware design.
• Unique Representation of Zero: Two's complement has only one representation for zero, unlike some other methods (like sign-magnitude) which have both +0 and -0.
• Efficient Hardware Implementation: The arithmetic logic unit (ALU) in a computer can directly handle two's complement numbers without needing separate logic for positive and negative signs.