Computer Science Fundamentals

Addressing Capability of 64-bit Systems

• A 64-bit system can theoretically address 2⁶⁴ bytes of memory.
• 2⁶⁴ unique addresses are possible in a 64-bit system.
• 16 exabytes is equivalent to 16,384 terabytes.
• A 64-bit system can theoretically address 16 exabytes of memory.
• 64-bit systems can address a significantly larger amount of memory compared to 32-bit systems, which can only address up to 4 GB.

Two's Complement Representation

• The two's complement representation of the decimal number 7 in an 8-bit format is 0000 0111.
• To find the two's complement of a positive integer, invert all the bits and add 1.
• The two's complement representation of -7 in an 8-bit format is 1111 1001.
• The two's complement system allows representing both positive and negative numbers using the same range of bits.
• To obtain the negative counterpart of a number in two's complement, invert all the bits and add 1 to the binary representation.

ASCII Encoding

• Standard ASCII (American Standard Code for Information Interchange) can only represent 128 characters.
• Extended ASCII expands on the standard set, allowing for the representation of up to 256 characters.
• Extended ASCII provides a benefit over standard ASCII by supporting a greater range of characters, including accented letters and special symbols.
• Extended ASCII allows for the representation of more characters, including accented letters, special symbols, and characters from other languages.
• The limitation of basic ASCII hinders communication and data representation, particularly for languages that require more than 128 characters.

Fixed-Point Representation

• Fixed-point representation emphasizes the fixed position of the fractional point in the number structure.
• Fixed-point representation is best suited for applications requiring high precision and where the range of values does not necessitate a floating-point representation.
• Fixed-point representations can be described as a number structure where the position of the decimal point is fixed.
• Fixed-point representation cannot effectively express a wide range of values, limiting its use in scenarios requiring significant dynamic range.

Gate Usage and Expressions

• The expression (𝐴 ⋅ 𝐵) + (𝐴 ⋅ 𝐶) uses four gates (two AND gates and one OR gate).
• The expression 𝐴 ⋅ (𝐵 + 𝐶) requires fewer gates than (𝐴 ⋅ 𝐵) + (𝐴 ⋅ 𝐶), as it only uses three (one AND gate and one OR gate).
• The expression 𝐴 ⋅ 𝐵 + 𝐶 uses more gates than 𝐴 ⋅ (𝐵 + 𝐶).
• The option suggesting (𝐴 ⋅ 𝐵) + (𝐴 ⋅ 𝐶) requires fewer gates than 𝐴 ⋅ (𝐵 + 𝐶) demonstrates an incorrect understanding of gate usage.
• The expression 𝐴 ⋅ (𝐵 + 𝐶) is logically equivalent to 𝐴 ⋅ 𝐵 + 𝐶.