Which of the following contains only valid octal digits?
0, 3, 5, 7
Every positional number system has a base (radix) that fixes how many distinct symbols it uses: the valid digits always run from 0 up to one less than the base. The octal system is base-8, so its complete digit set is 0, 1, 2, 3, 4, 5, 6, 7 — eight symbols in all. The symbols 8 and 9 simply do not exist in octal; the quantity we call eight is written as 108, just as ten is written 10 in decimal.
Checking each set for any digit greater than 7:
- The set 2, 4, 6, 9 contains 9, which is not an octal digit, so it is invalid.
- The set 3, 5, 7, 9 also contains 9, so it is invalid.
- The set 0, 3, 5, 7 has every digit less than or equal to 7, so all are legal octal digits — this is the correct choice.
- The set 1, 5, 7, 8 contains 8, which is not an octal digit, so it is invalid.
Octal is widely used in digital systems because each octal digit maps exactly onto a group of three binary bits (23 = 8), making it a compact shorthand for binary. Only the group 0, 3, 5, 7 satisfies the base-8 rule.
Important Questions from Types of Number System
The logic XOR operation of (4AC0) 16 and (B53F) 16 results________
How many bits are required to represent (1000) 10 in BCD code?
How many bits are needed to represent any decimal number between 0 and 2 n - 1 in base 2?
What is the Hexadecimal equivalent of 160?
Find out the decimal equivalent of (1011100) 2.
