Answer :
Answer:
Explanation:
To convert the hexadecimal number \( (38D)_{16} \) to decimal and binary:
1. **Decimal Conversion:**
\( (38D)_{16} \) represents a hexadecimal number. Each digit in hexadecimal corresponds to powers of 16.
\[ (38D)_{16} = 3 \times 16^2 + 8 \times 16^1 + D \times 16^0 \]
Now, convert \( D \) from hexadecimal to decimal:
- \( D \) in hexadecimal is equivalent to \( 13 \) in decimal.
Substitute and calculate:
\[ (38D)_{16} = 3 \times 256 + 8 \times 16 + 13 \times 1 \]
\[ (38D)_{16} = 768 + 128 + 13 \]
\[ (38D)_{16} = 909 \]
So, \( (38D)_{16} = 909 \) in decimal.
2. **Binary Conversion:**
To convert \( (38D)_{16} \) to binary, convert each hexadecimal digit to its 4-bit binary equivalent:
- \( 3_{16} = 0011_2 \)
- \( 8_{16} = 1000_2 \)
- \( D_{16} = 1101_2 \)
Combine these:
\[ (38D)_{16} = 0011 \ 1000 \ 1101_2 \]
Therefore, the conversions are:
- \( (38D)_{16} = 909_{10} \) in decimal.
- \( (38D)_{16} = 0011 \ 1000 \ 1101_2 \) in binary.