Enter Base 4 Values
Use only digits 0, 1, 2, and 3. Decimal points are allowed for fractional quaternary values.
Example Data Table
This table shows sample base 4 addition cases and their decimal checks.
| First Number | Second Number | Extra Number | Base 4 Sum | Decimal Check |
|---|---|---|---|---|
| 124 | 234 | — | 1014 | 6 + 11 = 17 |
| 1324 | 234 | — | 2214 | 30 + 11 = 41 |
| 10.24 | 2.14 | — | 12.34 | 4.5 + 2.25 = 6.75 |
| 3334 | 14 | 24 | 10024 | 63 + 1 + 2 = 66 |
Formula Used
Place value formula:
N = dn × 4n + dn-1 × 4n-1 + ... + d0 × 40
Fraction = d-1 × 4-1 + d-2 × 4-2 + ...
Base 4 addition uses the same column method as decimal addition. The difference is the carrying rule. In decimal, a carry happens when a column reaches ten. In base 4, a carry happens when a column reaches four. Each result digit must be 0, 1, 2, or 3.
For each column, the calculator adds all digits and the incoming carry. The result digit is the column total modulo 4. The outgoing carry is the column total divided by 4, using whole-number division.
Column rule:
result digit = column total mod 4
carry = floor(column total / 4)
How to Use This Calculator
- Enter the first base 4 number.
- Enter the second base 4 number.
- Add more values in the optional box when needed.
- Use digits 0, 1, 2, and 3 only.
- Add decimal points for fractional base 4 values.
- Select decimal proof places for checking.
- Press the calculate button.
- Review the sum, carry work, and downloads.
Understanding Base 4 Addition
What Base 4 Means
Base 4 is also called quaternary notation. It uses four symbols. These symbols are 0, 1, 2, and 3. Every place is a power of four. The first place on the right is 4^0. The next place is 4^1. Then comes 4^2, and so on. Fractional places move in the other direction. They use 4^-1, 4^-2, and smaller powers.
Why Carries Matter
Carries are the main idea in base 4 addition. A column cannot show a digit of 4 or higher. When a column total reaches 4, one group moves left. The remaining value stays in the current column. For example, 3 plus 2 equals 5 in decimal. In base 4, that becomes 11. The current column keeps 1. The next column receives a carry of 1.
Why Decimal Proof Helps
Decimal proof gives a useful check. It converts every input into base 10. Then it compares the decimal total with the base 4 answer. This helps students find typing mistakes. It also helps programmers test number conversion logic. Teachers can use the carry table for classroom examples. The steps make each place visible. This removes guesswork from the answer.
Practical Uses
Base 4 appears in computing lessons and number theory tasks. It is also useful for place-value practice. Some digital systems group binary digits into pairs. Each pair can map to one base 4 digit. This calculator is useful for homework, worksheets, coding checks, and demonstrations. It supports whole and fractional values. It also handles more than two addends. The export buttons make results easy to save.
FAQs
1. What digits are allowed in base 4?
Base 4 allows only 0, 1, 2, and 3. Digits like 4, 5, or 9 are not valid because each place can hold only four possible values.
2. Can this calculator add fractional base 4 numbers?
Yes. You can enter values such as 10.2 or 23.13. The calculator aligns fractional places, adds columns from right to left, and shows the final base 4 result.
3. When does a carry happen in base 4 addition?
A carry happens when a column total is 4 or greater. The result digit is the remainder after division by 4. The carry moves to the next left column.
4. Why is decimal proof included?
Decimal proof confirms the answer in a familiar number system. It helps you compare the base 4 sum with its base 10 value and catch input mistakes.
5. Can I add more than two base 4 numbers?
Yes. Enter extra values in the optional box. You can separate them with spaces, commas, semicolons, or new lines. The calculator adds all valid entries together.
6. What does the carry work table show?
The carry table shows each place value, digits added, incoming carry, column total, result digit, and outgoing carry. It explains how the final answer was formed.
7. Can I download my result?
Yes. The CSV button downloads structured data for spreadsheets. The PDF button saves a readable report containing the result, decimal proof, and carry steps.
8. Is base 4 the same as binary?
No. Binary uses two digits, 0 and 1. Base 4 uses four digits, 0 through 3. However, one base 4 digit can represent two binary digits.