Solution: A decimal number system consists of 10 digits from 0 to 9.
The definition of base describes it as a quantity to represent the number of digits present in that particular number system.
Therefore, here, the base is 10.

Solution: The base 2 represents that the number is binary ,whereas, the base 10 represents that it is to be converted to the decimal format.
Conversion: 22 * 1 + 21 * 1 + 20 *0 = 6.

Solution: 2’s complement is obtained by adding 1 to the 1’s complement of the number.
Here, Binary of 15 = 1111
1’s complement of 15= 0000
2’s complement of 15= 0000+1=0001.

Solution: Another name for base is radix. Base refers to the number of digits that a particular number system consists of.
The base of decimal number system is 10, binary is 2 and so on.

Solution: Since the base is 2 , it could be easily guessed that the number is binary. Conversion: 2-1 * 1 + 2-2 * 0 + 2-3 * 1 = 0.625.

Solution: Signed Magnitude of a number is a representation to determine if the number is positive or negative.
If the MSB of a number is 0, the number is positive, else if it is 1 the number is negative.
Here, +3 = 00000011
-3= 100000011.

Solution: In a decimal number system, a number with both integer and a fractional part has digits raised to both positive and negative powers of 10 and not 2.
e.g. 22.34 = 2 * 101 + 2 * 100 + 3 * 10-1 + 4 * 10-2.

Solution: The hexadecimal representations are as follows:
10 : A
11 : B
12 : C
13 : D
14 : E
15 : F.

Solution: All the numbers except 99.9A are decimal numbers.
This number has a hexadecimal component A in it, therefore , it is not a valid decimal number.
The decimal equivalent of A is 10.

Solution: G is not a valid hexadecimal number. In this system, only representations from A to E are used to represent the numbers from 10 to 15. The base of the hexadecimal number system is 16.