Understanding Overflow and Representation Errors

The video tutorial covers binary representation and storage limits, explaining how numbers are stored using bits and the limitations of this method. It discusses the pattern of increasing numbers with more bits and introduces overflow errors, which occur when the number of bits is insufficient to represent a number. The tutorial also explains floating point and roundoff errors, highlighting how computers approximate non-integer values due to limited memory. The video concludes with a call to practice using Khan Academy problems.

Why can't computers store infinitely large numbers?

• Because they are not designed to handle numbers.

• Because they can only store text data.

• Because they have a fixed amount of storage.

• Because they can only store images.

What is the largest number you can represent with two bits?

• 2

• 3

• 4

• 5

How many numbers can be represented with four bits?

• 32

• 16

• 12

• 8

What is the formula to calculate the largest number that can be represented with 'n' bits?

• n^2 - 1

• 2^n - 1

• 2^n

• n^2

What is an overflow error?

• An error when a number is zero.

• An error when a number is negative.

• An error when a number is too large to be represented with the available bits.

• An error when a number is too small to be represented.

In a system using six bits for integers, which operation will cause an overflow error?

• 5 + 25

• 3 + 29

• 15 + 15

• 10 + 20

What is a floating-point roundoff error?

• An error when a number is negative.

• An error due to the inability to represent certain decimal numbers precisely.

• An error when a number is too small.

• An error when a number is too large.

Why can't 0.2 be represented exactly in binary?

• Because it is too large.

• Because it is a whole number.

• Because it is not a power of two.

• Because it is a negative number.

What happens when you add two slightly too big floating-point values?

• They produce a smaller value.

• They produce an exact value.

• They produce an error big enough to reach the next higher representable value.

• They cancel each other out.

Which of the following is true about binary floating-point representation?

• It can represent all decimal numbers exactly.

• It can only represent numbers less than one.

• It can only represent whole numbers.

• It can represent very large numbers and decimals but with limitations.