Octal and Hexadecimal Number Systems

In the field of computer science and digital electronics, different number systems are used to represent numbers. Two commonly used number systems are octal and hexadecimal.

Octal Number System:
The octal number system is a base-8 system, meaning it uses 8 digits (0-7) to represent numbers. Each digit in the octal system represents a power of 8.

Hexadecimal Number System:
The hexadecimal number system is a base-16 system, meaning it uses 16 digits (0-9 and A-F) to represent numbers. Each digit in the hexadecimal system represents a power of 16.

Conversion from Hexadecimal to Octal:

To convert a hexadecimal number to its octal equivalent, we need to follow these steps:

1. Group the hexadecimal number into sets of 3 digits from right to left.
- If the number of digits is not a multiple of 3, add leading zeros to form complete sets of 3 digits.
2. Write down the octal equivalent of each group of 3 digits.
- Use the following table to find the octal equivalent of each hexadecimal digit:

Hexadecimal | Octal
------------|------
0 | 0
1 | 1
2 | 2
3 | 3
4 | 4
5 | 5
6 | 6
7 | 7
8 | 10
9 | 11
A | 12
B | 13
C | 14
D | 15
E | 16
F | 17

3. Combine the octal equivalents of each group to get the final octal equivalent.

Conversion of Hexadecimal 100 to Octal:

In this case, the hexadecimal number is 100. Let's convert it to octal:

1. Group the digits into sets of 3: 1|00.
2. Find the octal equivalent of each group: 1 -> 1, 00 -> 0.
3. Combine the octal equivalents: 10.
4. The octal equivalent of hexadecimal 100 is 10.

So, the correct answer is option A: 400.