To determine the next whole number after "A3DD" in the base-fourteen (base-14) system, let's break it down and solve it step by step.

1. Understand the base-14 system

In the base-14 system, the digits range from 0 to 13. For readability, we can use the following symbols:

• Digits 0 to 9 remain the same (0, 1, 2, ..., 9).
• 10 is represented as 'A'.
• 11 is represented as 'B'.
• 12 is represented as 'C'.
• 13 is represented as 'D'.

2. Interpreting the given number "A3DD"

The number "A3DD" is a four-digit number in base-14, where each letter represents a digit in this base:

• A = 10
• 3 = 3
• D = 13
• D = 13

Thus, "A3DD" corresponds to the base-14 digits (10, 3, 13, 13).

3. Finding the next whole number

We want to find the next number after "A3DD". In base-14, we apply addition similarly to the decimal system, but with a base of 14.

We start by incrementing the last digit:

• The last digit is "D" (13). Adding 1 to 13 gives 14, but since we're in base-14, 14 becomes 0 and causes a carry to the next digit.

The second-to-last digit is also "D" (13). Adding the carry from the previous step gives us:

• 13 + 1 = 14, which also becomes 0 with another carry to the next digit.

The third digit is "3". Adding the carry from the previous step gives us:

• 3 + 1 = 4.

The first digit "A" (10) remains unchanged since there was no carry at that level.

4. Result

Thus, the next number after "A3DD" in base-14 is:

• A400.

Would you like any more details on this calculation or have any questions?

Related Questions:

1. How do you convert base-14 numbers to base-10?
2. How would you subtract two numbers in the base-14 system?
3. What is the significance of non-standard bases, like base-14, in mathematics?
4. How do we perform multiplication in base-14?
5. Can you explain how carries work in different base systems?

Tip:

When working with non-standard bases, always remember to adjust for carry and place value changes based on the base you're using.