Convert `(756)_(16)` to decimal.

Answer

To convert the hexadecimal number \( (756)_{16} \) to decimal, we can follow these steps:

### Step 1: Identify the digits and their positions
The hexadecimal number \( 756 \) consists of three digits: 7, 5, and 6. In hexadecimal, the rightmost digit is at position 0, the next one to the left is at position 1, and so on. Thus, we have:
- \( 7 \) is in position 2
- \( 5 \) is in position 1
- \( 6 \) is in position 0

### Step 2: Convert each digit to decimal
We will convert each digit by multiplying it by \( 16 \) raised to the power of its position:
- For the digit \( 7 \):
\[ 7 \times 16^2 \]
- For the digit \( 5 \):
\[ 5 \times 16^1 \]
- For the digit \( 6 \):
\[ 6 \times 16^0 \]

### Step 3: Calculate the powers of 16
Now we calculate the powers of \( 16 \):
- \( 16^2 = 256 \)
- \( 16^1 = 16 \)
- \( 16^0 = 1 \)

### Step 4: Multiply each digit by its corresponding power of 16
Now we can perform the multiplications:
- For \( 7 \):
\[ 7 \times 256 = 1792 \]
- For \( 5 \):
\[ 5 \times 16 = 80 \]
- For \( 6 \):
\[ 6 \times 1 = 6 \]

### Step 5: Add the results together
Now, we add all the results together to get the decimal equivalent:
\[ 1792 + 80 + 6 = 1878 \]

### Final Result
Thus, the decimal equivalent of \( (756)_{16} \) is \( (1878)_{10} \).

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