MCQ
Q.
Conversion of an octal number $73_8$ to binary number is
Correct Answer: D
The correct answer is The conversion of the octal number $73_8$ to binary is $111011_2$. This is because in the octal system, each digit can have 8 different values (0-7), and when converted to binary, each octal digit is represented by 3 binary digits. The octal number $73_8$ can be broken down into its binary equivalent by first converting each digit into its binary form: $7_8 = 111_2$ and $3_8 = 011_2$. Combining these gives us $111011_2$..
🔑 Key Points
- The octal number system is base 8, using digits 0-7.
- To convert from octal to binary, each octal digit is replaced by its 3-digit binary equivalent.
🧮 Step-by-Step Solution
To convert $73_8$ to **binary**, we first find the binary representation of each digit: $7_8$ = \( 7 = 4 + 2 + 1 = 2^2 + 2^1 + 2^0 \) = $111_2$ and $3_8$ = \( 3 = 2 + 1 = 2^1 + 2^0 \) = $011_2$. Then, we combine these to get the binary representation of $73_8$ as $111011_2$.
📄 Additional Information
- Understanding the relationship between different number systems (binary, octal, decimal, hexadecimal) is crucial in computer science and programming. The binary system (base 2) is the foundation of computer programming, as it represents the two states of a digital switch (on or off). The octal system is sometimes used as a shorthand for binary, as it can represent binary numbers using fewer digits.