(3ab4)4

Jasonbradley

3 min read

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Jun 16, 2024

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What is (3ab4)4?

(3ab4)4 represents a number in base 4. Base 4, also known as quaternary, is a numeral system that uses only four distinct digits: 0, 1, 2, and 3.

Let's break down what (3ab4)4 means:

• ( )4: This indicates that the number is in base 4.
• 3ab4: These are the individual digits of the number.

To understand the value of this number, we need to convert it to base 10 (our usual decimal system):

Converting from Base 4 to Base 10

Each digit in a base 4 number represents a power of 4, starting from the rightmost digit as 4^0 (which is 1), then 4^1 (which is 4), 4^2 (which is 16), and so on.

Here's how we can convert (3ab4)4 to base 10:

(3ab4)4 = (3 * 4^3) + (a * 4^2) + (b * 4^1) + (4 * 4^0)

Note: The letters a and b represent unknown digits. To get the exact decimal value, we need to know what digits a and b stand for.

Example:

Let's assume a = 2 and b = 1. Then the conversion would be:

(3214)4 = (3 * 4^3) + (2 * 4^2) + (1 * 4^1) + (4 * 4^0) = (192) + (32) + (4) + (4) = 232

Therefore, if a = 2 and b = 1, then (3ab4)4 is equivalent to 232 in base 10.

Key Takeaway:

(3ab4)4 is a base 4 number with unknown digits a and b. To determine its decimal value, we need to know the values of these digits and apply the conversion process described above.