In a number system, if the base is increased, what happens to the number of uniq

₹0.0

Question: In a number system, if the base is increased, what happens to the number of unique digits available?

Options:

Correct Answer: It increases.

Solution:

Increasing the base of a number system increases the number of unique digits available for representation.

In a number system, if the base is increased, what happens to the number of unique digits available?

In a number system, if the base is increased, what happens to the number of unique digits available?

Step 1: Understand what a base is in a number system. The base (or radix) is the number of unique digits, including zero, that a number system uses.
Step 2: Identify the current base of the number system. For example, in base 10 (decimal), the unique digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which gives us 10 unique digits.
Step 3: Consider what happens when you increase the base. For example, if you change from base 10 to base 16 (hexadecimal), you add more unique digits.
Step 4: List the unique digits in the new base. In base 16, the unique digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, which gives us 16 unique digits.
Step 5: Conclude that increasing the base allows for more unique digits to be used in the number system.

Base of a Number System – The base of a number system determines how many unique digits can be used to represent numbers. For example, base 10 (decimal) uses digits 0-9, while base 2 (binary) uses digits 0 and 1.
Unique Digits – The unique digits available in a number system are directly related to its base; an increase in base allows for more unique digits.