A binary number is to be transformed by appending three 0s to the end of the number. For example, 11101 is transformed to 11101000. Which of the following correctly describes the relationship between the transformed number and the original number?
a. The transformed number is 8 times the value of the original number.
b. The transformed number is 3 times the value of the original number.
c. The transformed number is 4 times the value of the original number.
d. The transformed number is 1,000 times the value of the original number.

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Answer:

A. 8 times

Explanation:

Numbers can be converted from one base to another base. a. The transformed number is 8 times the value of the original number.

Given that:

Three 0s are appended to a binary digit to get a new binary digit.

Using the given values, the transformation can be illustrated as follows:

[tex]11101000_2 \to 11101_2 \times 1000_2[/tex]

Where:

[tex]1000_2[/tex] represents the three appended 0s.

In binary [tex]1000_2[/tex] represents 8 in decimal.

So, the above illustration can be expressed as:

[tex]11101000_2 \to 11101_2 \times 8_{10}[/tex]

This means that the new or transformed number is 8 times the original number.

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