Numbers and Arithmetic Extension Assignment
For this assignment, you will explore number bases, complements, shifting, and floating-point calculations. Internally, computers utilize complements and shifts to implement integer mathematical operations on binary numbers. Today’s systems also follow the IEEE 754 standard for floating-point arithmetic when non-integer numbers are required.
Background Material
Internally, computers utilize logic circuits to implement arithmetic operations on binary (base two) numbers. Two completely different sets of circuits are used: one set handles integer arithmetic, while another hardware component handles floating-point numbers (which are crude approximations of real numbers). In order to make computers compatible with one another, certain standards exist for defining how mathematical operations will be implemented.
To begin your journey of understanding how computers do math, see my Numbers and Arithmetic OER materials.
Requirements
Prepare a video presentation in MP4 or WEBM format that covers the following topics:
- Explain the differences between decimal, binary, octal, and hexadecimal.
- Demonstrate conversion from a hexadecimal number to decimal. Show all work.
- Demonstrate conversion from a binary number to decimal. Show all work.
- Using 4 pairs of randomly generated integers, demonstrate subtraction using nine’s complement arithmetic. Show all work for all 4 subtraction examples.
- Explain how shifting works. Remember to distinguish between logical and arithmetic right shifts.
- Summarize the IEEE 754 standard. Be sure to mention precision levels, the number of representations for zero, the parts of a number in IEEE 754, and subnormal numbers.
- Distinguish between hard float architectures and soft float architectures.
- Give a specific manufacturer and model of a CPU that contains a floating point unit.
- Give a specific manufacturer and model of a CPU that uses a soft float architecture.
Grading
Please review the Numbers and Arithmetic Extension Rubric before submitting this Extension Assignment.
As explained in the course syllabus, a minimum grade of 70 is required to receive any partial credit for this assignment. A minimum grade of 85 is required to be able to attempt the Challenge Assignment later in the semester.
