How to solve step by step hexa to decimal 4 bits

To convert a 4-bit hexadecimal number to a decimal number, follow these steps:

### 1. **Understand the Hexadecimal System:**
   - The hexadecimal (hex) system is base-16, meaning it uses 16 different symbols (0-9 and A-F).
   - Each hex digit represents 4 bits. The hex digits are:
     - `0` = 0000 (binary) = 0 (decimal)
     - `1` = 0001 (binary) = 1 (decimal)
     - `2` = 0010 (binary) = 2 (decimal)
     - `3` = 0011 (binary) = 3 (decimal)
     - `4` = 0100 (binary) = 4 (decimal)
     - `5` = 0101 (binary) = 5 (decimal)
     - `6` = 0110 (binary) = 6 (decimal)
     - `7` = 0111 (binary) = 7 (decimal)
     - `8` = 1000 (binary) = 8 (decimal)
     - `9` = 1001 (binary) = 9 (decimal)
     - `A` = 1010 (binary) = 10 (decimal)
     - `B` = 1011 (binary) = 11 (decimal)
     - `C` = 1100 (binary) = 12 (decimal)
     - `D` = 1101 (binary) = 13 (decimal)
     - `E` = 1110 (binary) = 14 (decimal)
     - `F` = 1111 (binary) = 15 (decimal)

### 2. **Write Down the Hex Number:**
   - Let's say the hex number is `A3F`. It is actually 12 bits long (but we focus only on 4 bits at a time).
   - If it’s a 4-bit number, you might have something like `F`.

### 3. **Convert Each Hex Digit to Binary:**
   - Convert the hex digit `F` to binary.
     - `F` = 1111 in binary.
   - So, for a 4-bit system, `F` is `1111` in binary.

### 4. **Convert the Binary Number to Decimal:**
   - Now, convert the binary number `1111` to decimal.
   - To convert, multiply each bit by 2 raised to the power of its position from right (starting at 0):
     \[
     1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0
     \]
     \[
     = 8 + 4 + 2 + 1 = 15
     \]
   - Therefore, `F` in hex equals `15` in decimal.

### 5. **Final Result:**
   - For a 4-bit hexadecimal number, `F` in hex is `15` in decimal.

### Example
Let's take another example with the hex digit `C`:
   - `C` = 1100 in binary.
   - Convert `1100` to decimal:
     \[
     1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0
     \]
     \[
     = 8 + 4 + 0 + 0 = 12
     \]
   - Therefore, `C` in hex equals `12` in decimal.

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Would you like more details or have any questions? 

Here are some related questions:
1. How do you convert a larger hexadecimal number (e.g., 16-bit) to decimal?
2. What is the process to convert a decimal number to hexadecimal?
3. How do binary and hexadecimal systems relate to each other?
4. How can you perform arithmetic operations directly in hexadecimal?
5. What are common uses of hexadecimal in computing?

**Tip:** When converting hexadecimal to decimal, breaking it down to binary first can simplify the process, especially for smaller bit-sized numbers like 4-bit or 8-bit values.

Learn how to convert a 4-bit hexadecimal number to a decimal value with a step-by-step solution. This guide covers key concepts in number systems, including hexadecimal to binary conversion and binary to decimal calculation. Ideal for students in Grades 9-12.

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