Understanding Normalized Floating Point Binary

This video is the second part of a series on floating point binary, focusing on normalization. It explains how to represent numbers consistently using normalized floating point binary, ensuring accuracy. The video provides examples of converting numbers to base 10 and demonstrates the process of storing both positive and negative numbers in this format. Key concepts include the importance of normalization for consistent representation and accuracy, with practical examples of storing numbers like 6.5, 2.25, -2.5, and -0.25. The video concludes with key questions to reinforce understanding.

What is the main issue with having multiple binary representations for the same number?

• It increases the storage space required.

• It makes calculations faster.

• It allows for more accurate calculations.

• It leads to inconsistency in data representation.

Why is normalization important in floating point binary representation?

• To make the numbers easier to read.

• To ensure a consistent and accurate representation.

• To reduce the number of bits used.

• To increase the range of numbers that can be represented.

How can you identify a positive normalized floating point binary number?

• It ends with 1 0.

• It starts with 0 1.

• It ends with 0 1.

• It starts with 1 0.

In the example of converting 6.5, what is the exponent in the normalized floating point binary representation?

• 1

• 2

• 4

• 3

What is the first step in converting a base 10 number to normalized floating point binary?

• Convert the number to two's complement.

• Determine the exponent.

• Write the number in fixed point binary.

• Normalize the mantissa.

When converting 2.25 to normalized floating point binary, how many places is the binary point moved to the left?

• 2

• 4

• 1

• 3

What is the exponent for the normalized floating point binary representation of 2.25?

• 1 0 0

• 1 1 0

• 0 1 0

• 0 0 1

How do you convert a positive binary number to its negative counterpart in two's complement?

• Subtract one from the number.

• Copy bits up to the first one, then invert the rest.

• Add one to the number.

• Invert all bits.

In the example of converting -2.5, what is the exponent in the normalized floating point binary representation?

• 1 1 0

• 0 1 0

• 1 0 0

• 0 0 1

What is the correct representation of -0.25 in normalized floating point binary?

• 1 0 1 1 0 0 0 0

• 1 1 1 0 0 0 0 0

• 1 1 0 1 0 0 0 0

• 1 0 0 1 1 0 0 0