Errors and Representations in Computing

The video tutorial covers the limitations of storing numbers in binary, focusing on overflow and round-off errors. It explains how variables and mathematical expressions are used in coding, and discusses precision and rounding differences in calculations. The tutorial also explores integer overflow in bit representation and analyzes floating point arithmetic errors.

What is a limitation of storing numbers in binary?

• Binary can represent infinite numbers.

• Binary storage is not used in computers.

• Binary storage is limited by the number of bits.

• Binary numbers are always accurate.

What is an overflow error?

• When a number is too large for the system to handle.

• When a number is stored as a string.

• When a number is too small to be represented.

• When a number is perfectly represented.

What causes a round-off error?

• When the decimal part is too long to be stored.

• When a number is stored as an integer.

• When a number is too large.

• When a number is too small.

What is a rational number?

• A number with no decimal part.

• A number that can be expressed as a ratio of two integers.

• A number that cannot be expressed as a fraction.

• A number that is always positive.

What does floating-point representation mean?

• A way to store binary data.

• Scientific notation used by computers.

• A way to store only integers.

• A method to store text data.

In the example problem, what is the initial value of the radius?

• 3.14

• 14.12

• 0.5

• 33.27

Why might two computers give slightly different results for the same calculation?

• Different operating systems.

• Different screen resolutions.

• Different keyboard layouts.

• Different levels of precision in representing constants like Pi.

What is the maximum number that can be represented with five bits?

• 32

• 31

• 63

• 15

What issue did YouTube face with Gangnam Style's view count?

• The video was deleted.

• The view count was too high for a 32-bit signed integer.

• The video was not popular.

• The view count was negative.

What is a round-off error in floating-point arithmetic?

• An error due to incorrect data type.

• An error due to limited precision in representing decimal numbers.

• An error due to a number being too small.

• An error due to a number being too large.