Solution: The maximum value in any number system is one less than the value of the base. The base in an octal number system is 8, therefore, the maximum value of the single digit is 7. It takes digits from 0 to 7.

Solution: In a number system, every digit is denoted by a specific power of base. Like in an octal system, consider the number 113, it will be represented as :
82 * 1 + 81 * 1 + 80 *3.

Solution: The octal number system comprises of only 8 digits. Hence, three bits (23 = 8) are sufficient to represent any octal number in the binary format.

Solution: Certain binary to octal representations are :
000=0
001=1
010=2
011=3
100=4
101=5
110=6
111=7.

Solution: To convert an octal number to decimal number:
81 * 2 + 80 * 2 = 16 + 2 = 18.
Hence, the decimal equivalent is 18.

Solution: To obtain the octal equivalent, we take numbers in groups of 3, from right to left as :
 000  010  010   100
 
  0    2    2      4     =  (224)8.

Solution: Octal subtraction is done as follows:
417
– 232
________
165
The octal subtraction is the same as that of any other number system. The only difference is, like in a decimal number system, we borrow a group of 10, in a binary system we borrow a group of 2, in an octal number system, we borrow in groups of 8.

Solution: The 1’s complement of a number is obtained by reversing the bits with value 1 to 0 and the bits with value 0 to 1.
Here, 0.101 gets converted to 1.010 in its 1’s complement format.

Solution: To convert octal to hexadecimal, we first write binary format of the number and then make groups of 4 bits from right to left, as follows:
 5     4      0     1
101   100    000    001   (octal -> binary)
1011     0000    0001     ( groups of 4)
B         0       1       ( hexadecimal equivalent)
Therefore, the hexadecimal equivalent is (B01)16.

Solution: The first bit is the sign bit whereas the rest of the bits are magnitude bits. So the number is: 0010 = 21 * 1 =2
But, the sign bit is 1, Therefore the answer is : (-2)10.