20 Fixed Point Arithmetic Interview Questions and Answers

Fixed Point Arithmetic is a type of mathematics that is used in digital signal processing and computer programming. It is often used in embedded systems where the limited resources make it necessary to use a more efficient form of arithmetic. Fixed Point Arithmetic is a specialized topic, and as such, you may be asked questions about it during a technical interview. In this article, we review some of the most common Fixed Point Arithmetic questions and how you should answer them.

Fixed Point Arithmetic Interview Questions and Answers

Here are 20 commonly asked Fixed Point Arithmetic interview questions and answers to prepare you for your interview:

1. What is fixed point arithmetic?

Fixed point arithmetic is a type of numerical analysis that allows for the representation of fractional values using a fixed number of bits. This can be useful for things like audio or video processing, where fractional values are common but a limited number of bits is available.

2. Can you explain what a fixed point number is?

A fixed point number is a number that has a set number of digits after the decimal point. This is in contrast to a floating point number, which can have a variable number of digits after the decimal point. Fixed point numbers are often used in computer programming because they can be more easily represented in binary form.

3. How are floating-point numbers different from fixed-point numbers?

Floating-point numbers are stored in scientific notation, meaning that they are represented by a mantissa and an exponent. This allows for a much wider range of numbers to be represented, but at the cost of precision. Fixed-point numbers, on the other hand, are represented by a number of bits that are allocated for the integer part and the fractional part. This gives fixed-point numbers much more precision, but at the cost of range.

4. What are the advantages and disadvantages of using fixed-point arithmetic over floating-point? Which one would you recommend for use in data science?

The main advantage of fixed-point arithmetic is that it is much more efficient than floating-point, since it doesn’t require the extra step of normalization. Fixed-point also doesn’t suffer from rounding errors, which can be a problem with floating-point. However, fixed-point can only represent a limited range of numbers, so it is not suitable for all applications. In general, I would recommend using fixed-point for data science applications where efficiency is important and the data can be accurately represented using a limited range.

5. Why is it necessary to perform scaling on variables when converting them to fixed-point format?

When you are dealing with fixed point arithmetic, it is important to scale your variables so that they fit within the specified number of bits. Otherwise, you run the risk of losing precision and accuracy in your calculations.

6. Can you explain the difference between signed and unsigned integer formats?

Signed integers can represent both positive and negative numbers, while unsigned integers can only represent positive numbers. The most significant bit (MSB) of a signed integer is used to represent the sign of the number (0 for positive, 1 for negative), while the MSB of an unsigned integer is always 0. This means that the range of numbers that can be represented by a signed integer is half that of an unsigned integer. For example, an 8-bit signed integer can represent numbers between -128 and 127, while an 8-bit unsigned integer can represent numbers between 0 and 255.

7. How many bits are required to represent an N-bit binary number?

The number of bits required to represent an N-bit binary number is N+1.

8. Can you explain how overflow occurs in fixed-point calculations?

Overflow occurs in fixed-point calculations when the result of a calculation is too large to be represented within the available number of bits. This can happen when two large numbers are added together, for example, and the result exceeds the maximum value that can be represented. Overflow can also occur when a number is multiplied by a very large number, resulting in a number that is too large to be represented.

9. What do you understand about truncation errors? How can they be avoided?

Truncation errors are a type of error that can occur when converting a number from one data type to another, usually when converting a floating point number to an integer. The error occurs because the decimal portion of the number is truncated, or cut off, when it is converted. This can lead to inaccuracies in the final number. Truncation errors can be avoided by using a data type that can accurately represent the number, such as a double instead of an int.

10. What’s the best way to convert from fractional or decimal form to integer representation?

The best way to convert from fractional or decimal form to integer representation is to use a fixed point arithmetic library. This library will provide you with the necessary functions to accurately convert between the two forms.

11. What do you know about bit twiddling? Is it possible to add two integers without using +, ++, -, –, *, /, % operators? If yes, then how?

Bit twiddling is the process of manipulating data at the bit level. It is often used to optimize code or to perform operations that would be otherwise impossible. It is possible to add two integers without using any of the aforementioned operators by utilizing bitwise operators instead.

12. What does saturation mean in context with digital signal processing?

Saturation is the process of limiting the range of a signal. In digital signal processing, this is often done to prevent distortion.

13. What’s the best way to avoid rounding errors when performing multiplication operations on fixed-point numbers?

There are a few ways to avoid rounding errors when performing multiplication operations on fixed-point numbers. One way is to ensure that both numbers being multiplied are scaled to the same precision. Another way is to perform the multiplication operation using a larger data type than the original numbers, and then truncate the result back to the original data type.

14. Can you give me some examples where fixed-point arithmetic is used in data science?

Fixed-point arithmetic is often used in data science when working with large numbers or when precision is important. For example, when working with large numbers, fixed-point arithmetic can help prevent rounding errors. Additionally, fixed-point arithmetic can be used when performing calculations that require a high degree of precision, such as when working with financial data.

15. Can you describe the steps involved in adding two N-bit fixed-point numbers manually?

In order to add two N-bit fixed-point numbers, you first need to align them so that the decimal points are in the same place. Once they are aligned, you can simply add the numbers together digit by digit, starting from the rightmost digit and working your way to the left. If the sum of any two digits is greater than or equal to 10, then you will need to carry over the 1 to the next digit to the left.

16. What is your opinion on the use of fixed-point arithmetic in embedded systems?

I believe that fixed-point arithmetic can be very useful in embedded systems, as it can provide a more efficient way to perform calculations while still maintaining a high degree of accuracy. However, it is important to be aware of the potential pitfalls of using fixed-point arithmetic, as it can sometimes lead to unexpected results if not used correctly.

17. What is your opinion on the roundoff error compensation technique?

I believe that the roundoff error compensation technique is a great way to improve the accuracy of fixed point arithmetic. This technique can help to reduce the error that can occur when rounding numbers.

18. What do you think are the major differences between fixed-point and floating-point processors?

The main difference between fixed-point and floating-point processors is the way in which they store and process numbers. Fixed-point processors store numbers as a series of bits, while floating-point processors store numbers in a more complex format that includes a mantissa and an exponent. This means that fixed-point processors are more limited in the range of numbers that they can represent, but they are also faster and more efficient.

19. Can you explain the concept of guard digits? How can they help improve accuracy?

Guard digits are an extra digit added to the end of a number to help protect against rounding errors. When a number is rounded, the guard digit helps to ensure that the number is rounded to the correct value. This can help improve accuracy by ensuring that numbers are not rounded incorrectly.

20. Can you provide some examples of applications that use fixed-point arithmetic?

Fixed-point arithmetic is often used in applications where a high degree of accuracy is required, such as in financial or scientific calculations. It can also be used in real-time systems where timing is critical, such as in control systems or audio processing.