Converting Octal to Decimal Numbers

This video tutorial explains how to convert octal numbers, including fractional ones, into decimal numbers. It begins with a simple example of converting the octal number 370 to decimal, followed by more complex examples such as 1071 and 16475. The tutorial also covers the conversion of fractional octal numbers, like 425.28, into decimal form. Each example is broken down step-by-step, demonstrating the multiplication of each digit by powers of 8 and summing the results to achieve the final decimal number.

What is the first step in converting an octal number to a decimal number?

• Multiply each digit by 8 raised to the power of its position.

• Divide each digit by 8.

• Add all the digits together.

• Multiply each digit by 10 raised to the power of its position.

In the example of converting 370 from octal to decimal, what is the value of 3 times 8 squared?

• 256

• 64

• 192

• 24

When converting 1071 from octal to decimal, what is the value of 1 times 8 cubed?

• 64

• 512

• 128

• 256

What is the decimal equivalent of the octal number 1071?

• 569

• 671

• 512

• 1024

In the conversion of 16475 from octal to decimal, what is the value of 6 times 8 cubed?

• 2048

• 512

• 3072

• 4096

What is the decimal equivalent of the octal number 16475?

• 7485

• 6574

• 8457

• 5748

How do you handle the fractional part when converting a fractional octal number to decimal?

• Multiply by 8 raised to a positive power.

• Add the fractional part directly.

• Multiply by 8 raised to a negative power.

• Divide by 8 raised to a positive power.

What is the decimal equivalent of the fractional octal number 425.28?

• 277.375

• 300.25

• 200.375

• 256.125

In the conversion of 425.28 from octal to decimal, what is the value of 2 times 8 to the negative 1?

• 0.125

• 0.75

• 0.25

• 0.5

What is the value of 8 to the negative 2 in the conversion of a fractional octal number?

• 0.125

• 0.25

• 0.5

• 0.0625