Computer Science Fundamentals

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Questions and Answers

What is the theoretical maximum memory a 64-bit system can address?

256 gigabytes

32 petabytes

4 terabytes

16 exabytes (correct)

How many unique addresses can a 64-bit system theoretically have?

2^48

2^128

2^64 (correct)

2^32

What is the equivalent of 16 exabytes in terabytes?

4,000 terabytes

16,000 terabytes (correct)

1,000 terabytes

64,000 terabytes

Which type of system is capable of theoretically addressing 16 exabytes of memory?

64-bit system Signup and view all the answers

Compared to a 32-bit system, how does a 64-bit system's addressing capability differ?

It can address more memory. Signup and view all the answers

What is the two's complement representation of the decimal number 7 in an 8-bit format?

0000 0111 Signup and view all the answers

How is the two's complement of a positive integer calculated?

Invert the bits, then add 1 Signup and view all the answers

What is the two's complement representation of -7 in an 8-bit format?

1111 1001 Signup and view all the answers

Which of the following correctly describes the two's complement system?

It can accurately perform arithmetic operations. Signup and view all the answers

If the binary representation of a number is 0000 0111, what process leads to its negative counterpart in two's complement?

Invert the bits, then add 1 Signup and view all the answers

What is a primary limitation of the standard ASCII character encoding?

It represents only English letters. Signup and view all the answers

How does extended ASCII improve upon the basic ASCII set?

By using 8 bits to represent more characters. Signup and view all the answers

What is the primary benefit of using extended ASCII over standard ASCII?

It can encode a wider variety of characters. Signup and view all the answers

Which of the following statements about extended ASCII is true?

It can represent a total of 256 characters. Signup and view all the answers

Why is the limitation of basic ASCII significant in computing?

It restricts character representation across multiple languages. Signup and view all the answers

What does fixed-point representation emphasize in its structure?

A set number of digits after the decimal point Signup and view all the answers

Which statement about fixed-point representation is true?

It is limited to a predefined decimal precision. Signup and view all the answers

In which situation is fixed-point representation most beneficial?

In applications with consistent fractional precision Signup and view all the answers

Fixed-point representations can be described as what type of number structure?

Static with predetermined decimal positions Signup and view all the answers

Which of the following is a limitation of fixed-point representation?

It can lead to overflows when the number exceeds the fixed range. Signup and view all the answers

Which expression is simpler in terms of the number of gates used?

𝐴 ⋅ 𝐵 + 𝐶 Signup and view all the answers

How many gates are used in the expression (𝐴 ⋅ 𝐵) + (𝐴 ⋅ 𝐶)?

3 Signup and view all the answers

Which expression involves more gates?

(𝐴 ⋅ 𝐵) + (𝐴 ⋅ 𝐶) Signup and view all the answers

Which option demonstrates an incorrect understanding of the gate usage?

𝐴 ⋅ 𝐵 + 𝐶 uses three gates. Signup and view all the answers

Which of the following expressions is equivalent to 𝐴 ⋅ 𝐵 + 𝐶?

𝐵 ⋅ 𝐶 + 𝐴 Signup and view all the answers

Study Notes

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.

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Description

This quiz covers essential topics in computer science, including two's complement representation for negative numbers, fixed-point representation, and character encoding such as extended ASCII. It also discusses logic gates and their simplifications in digital circuits. Test your understanding of these fundamental concepts!