**The value of base in a decimal number system is***__*

**a) **8**b)** 2**c)** 10**d) **16

**Answer: (c) 10**

**Explanation: **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.

2. **Convert : (110)2 = ( __ )10 .**

**a) **4**b)** 5**c)** 6**d) **9

**Answer: (c) 6**

**Explanation: **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.

3.** The 2’s complement of 15 is __**

**a)** 0000**b)** 0001**c)** 0010**d)** 0100

**Answer: (b) 0001**

**Explanation: **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

4**. Another name for base is __**

**a) **root**b)** radix**c)** entity**d) **median

**Answer: (b) radix**

**Explanation: **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.

5. **The decimal equivalent of (0.101)2 will be __**

**a) **0.5**b)** 0.625**c) **0.25**d) **0.875

**Answer: (b) 0.625**

**Explanation: **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.

6.** The signed magnitude for -3 will be _**

**a)** 00000011**b)** 10000011**c) **11111101**d)** 11111100

**Answer: (b) 10000011**

**Explanation: **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.

7. **A number with both integer and a fractional part has digits raised to both positive and negative powers of 2 in a decimal number system.**

**a)** True**b)** False

**Answer: (b) False**

**Explanation:** 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.

8.** The hexadecimal representation of 14 is ___**

**a)** A**b)** F**c) **D**d) **E

**Answer: (d) E**

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

9. **Which of the following is not a decimal number?**

**a)** 114**b)** 43.47**c) **99.9A**d)** 1010

**Answer: (c) 99.9A**

**Explanation: **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.

10.** Select the incorrect option :**

**a) **(101)10 = (1100101)2

b) G is valid in hexadecimal system.**c) **C represents 12**d) **The base of a decimal number system is 10

**Answer: (b) G is valid in hexadecimal system.**

**Explanation: **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