11100110101 into base 10, base 8, base 16.

To convert the number 11100110101 into base 10, base 8, and base 16, you need to understand the positional notation system.

The positional notation system, also known as the "base" or "radix," determines how numbers are represented using different symbols and their positions. The most commonly used bases are base 10 (decimal), base 2 (binary), base 8 (octal), and base 16 (hexadecimal).

Let's convert 11100110101 into base 10, base 8, and base 16 step by step:

1. Base 10 (Decimal):
In base 10, each digit's value is multiplied by the corresponding power of 10. Starting from the rightmost digit, the powers of 10 increase from right to left.

1 × 10^10 + 1 × 10^9 + 1 × 10^8 + 0 × 10^7 + 0 × 10^6 + 1 × 10^5 + 1 × 10^4 + 0 × 10^3 + 1 × 10^2 + 0 × 10^1 + 1 × 10^0

= 11,100,110,101

So, 11100110101 in base 10 is 11,100,110,101.

2. Base 8 (Octal):
In base 8, each digit's value is multiplied by the corresponding power of 8. Starting from the rightmost digit, the powers of 8 increase from right to left.

The number 11100110101 can be grouped into sets of three digits from right to left, as follows:
11 100 110 101

Now convert each group of three digits into decimal:
(1 × 8^2) + (1 × 8^1) + (1 × 8^0) = 8 + 1 + 1 = 10

The decimal equivalent of each group is:
10 4 6 5

So, 11100110101 in base 8 is 10465.

3. Base 16 (Hexadecimal):
In base 16, the digits 0-9 represent their usual values, and the letters A-F represent values 10-15, respectively.

The number 11100110101 can be grouped into sets of four digits from right to left, as follows:
1 1100 1101 0101

Now convert each group of four digits into decimal:
(1 × 16^3) + (12 × 16^2) + (13 × 16^1) + (5 × 16^0) = 4096 + 3072 + 208 + 5 = 7381

The decimal equivalent of each group is:
1 C D 5

So, 11100110101 in base 16 is 1CD5.

Therefore, the conversions are as follows:
Base 10: 11,100,110,101
Base 8: 10,465
Base 16: 1CD5