1 – Computer Arithmetic

Easy Level Questions (10 Questions)

1.     Define a number system and briefly explain the significance of the binary number system in computer architecture. (5 Marks)

2.     List and briefly describe the four primary number systems used in computing. (5 Marks)

3.     Convert the decimal number 65(10) to its binary equivalent. Show all necessary steps. (5 Marks)

4.     Convert the binary number 101101(2) to its decimal equivalent. Show all necessary steps. (5 Marks)

5.     Convert the octal number 73(8) to its decimal equivalent. Show all necessary steps. (5 Marks)

6.     Convert the hexadecimal number 3F(16) to its decimal equivalent. Show all necessary steps. (5 Marks)

7.     What is Binary Coded Decimal? Explain its main advantage in specific applications. (5 Marks)

8.     Define ASCII. How many bits are typically used in standard ASCII, and what is its primary purpose in computing? (5 Marks)

9.     Perform the following binary addition: 11011(2) + 1010(2). Show all steps, including any carries generated. (5 Marks)

10.                        Perform the following binary subtraction using the direct subtraction method: 1110(2) – 101(2). Show all steps. (5 Marks)

Moderate Level Questions (7 Questions)

1.     Convert the decimal number 217(10) to its equivalent binary, octal, and hexadecimal representations. Clearly show the detailed steps for each conversion. (5 Marks)

2.     Convert the binary number 1101110101(2) to its octal and hexadecimal equivalents using the grouping method. Explain the rationale behind using this grouping method for these specific conversions. (5 Marks)

3.     Compare and contrast Binary Coded Decimal and pure binary representation. Discuss a scenario where BCD would be preferred over pure binary for data storage or processing. (5 Marks)

4.     Perform the binary subtraction: 10011(2) – 01010(2) using the 1’s complement method. Assume a 5-bit register for your calculation. Show all steps clearly. (5 Marks)

5.     Perform the binary subtraction: 11000(2) – 01101(2) using the 2’s complement method. Assume a 5-bit register for your calculation. Show all steps clearly. (5 Marks)

6.     Explain the fundamental advantage of using 2’s complement representation for performing subtraction in digital computers compared to direct subtraction. Provide a simple example to illustrate how 2’s complement simplifies hardware implementation. (5 Marks)