How to Convert from Base 10 to Base 4

TL;DR

Learn how to convert numbers to base 4 by repeatedly dividing and using remainders, with detailed steps and examples.

Transcript

in this problem we're going to convert this number to base 4. to do this we're going to just repeatedly divide by 4 and write down the remainders and the remainders will be our answer so we'll start by taking 1 1 0 to 8 and dividing by 4. so i'm going to put this into my calculator 1 1 0 2 8 divided by 4. so i got 2 7 5 7. so the remainder is 0 rig... Read More

Key Insights

• ⚾ Converting a number to base 4 involves dividing by 4 and noting remainders.
• ✖️ The decimal part of the division is multiplied by 4 to find the remainder.
• ⚾ The remainders in base 4 are always 0, 1, 2, or 3.
• 🪈 The final answer is obtained by writing the remainders in reverse order and adding a subscript 4.
• ❓ Following the step-by-step process ensures accuracy in conversion.
• ➗ Mental calculations can be used for simpler divisions.
• ❓ Writing down the steps is helpful to avoid mistakes when converting.

Questions & Answers

Q: How do you convert a number to base 4?

To convert a number to base 4, you divide it repeatedly by 4, noting the remainders at each step. The remainders will be the digits of the number in base 4.

Q: What do you do with the decimal part of the division?

The decimal part, if present, is multiplied by 4 to find the remainder. This remainder is then used as a digit in the base 4 representation of the number.

Q: Can you explain the process of converting a number to base 4 with an example?

Sure. Let's take the number 11028. Divide it by 4, note the remainder 0. Repeat the process with the whole number part, 2757, resulting in a remainder of 1. Continue dividing until the whole number part becomes 0, noting the remainders 2, 2, 3, 0, 1, 1. The final answer is 2230114 in base 4.

Q: Do the remainders in base 4 follow a pattern?

Yes, the remainders in base 4 are always 0, 1, 2, or 3. They repeat in a cyclical pattern as you divide the number by 4, and these remainders represent the digits in base 4 representation.

Summary & Key Takeaways

• The video explains how to convert a number to base 4 by dividing it repeatedly by 4 and noting the remainders.

• The process involves finding the whole number part of the division, multiplying the decimal part by 4 for the remainder, and repeating until the whole number part becomes 0.

• The remainders in base 4 are always 0, 1, 2, or 3, and the final answer is obtained by writing the remainders in reverse order and adding a subscript 4.