Hexadecimal Number System

**Category : **10th Class

The hexadecimal number system is based 16. Therefore, it means, there are 16 basic digits on which whole hexadecimal number system depends. The digits are 0,1, 2, 3, 4, 5, 6, 7, 8, 9,10,11, 12,13,14 and 15, whereas the numbers 10,11,12, 13, 14, and 15 are also represented as A, B, C, D, E and F. By using these 16 digits all the numbers in hexadecimal number system are written. Thus the place value in hexadecimal system is increased in the power of 16 from right to left.

**Converting Decimal Number into Hexadecimal**

While converting a decimal number into hexadecimal, you need to do the successive division of decimal number by 16 until the quotient becomes less than 16. In the end write the remainders in reverse order to get the desired results. The following example shows, how to convert 640 into hexadecimal:

Remainders in reverse order = 280 280 is the conversion of 640 into hexadecimal.

**Converting Hexadecimal Number into Decimal Number**

While converting hexadecimal number into decimal, you need to find out the place value of each digit of that number and add them. The following example shows how to convert 102F into decimal. First find the place value of each digit of the number 102F from right to left.

The following example shows the place value of each digit in the number 121FA:

Place value of A is: \[10*{{16}^{0}}=10\]

Place value of F is: \[15*{{16}^{1}}=240\]

Place value of 1 is: \[1*{{16}^{2}}=256\]

Place value of 2 is: \[2*{{16}^{3}}=8192\]

Place value of 1 is: \[1*{{16}^{4}}=65536\]

Sum of all the place values = 74234 = Decimal equivalent of 121FA.

**A system with base-10 is a decimal number system. Which one of the following is the correct conversion of 10001 into decimal?**

(A) 16

(B) 9

(C) 17

(D) 2

(E) None of these

**Answer: (c)**

Explanation

Correct Option:

(C) The place value of 1 is: \[1*{{2}^{0}}=1\]

The place value of 0 is: \[0*{{2}^{1}}=0\]

The place value of 0 is:\[0*{{2}^{2}}=0\]

The place value of 0 is: \[0*{{2}^{3}}=0\]

The place value of 1 is: \[1*{{2}^{4}}=16\]

The decimal number =1+0+0+0+16 =17

Incorrect Options:

Therefore, option (C) is correct and rest of the options is incorrect.

**The hexadecimal number system is based on 16. In the hexadecimal number system which one of the following digits does not exist?**

(A) 2

(B) 8

(C) 16

(D) 19

(E) None of these

**Answer: (d)**

Explanation

Correct Option:

(D) The hexadecimal number system is based on 0 to 15.

Incorrect Options:

Therefore, option (D) is correct and rest of the options is incorrect.

**Which of the following statements is/are true? **

**Statement A:** In hexadecimal number system C represents 13.

**Statement B:** In hexadecimal number system 14 represented as D.

(A) Statement A is correct

(B) Statement B is correct

(C) Both statement A and B are correct

(D) Neither statement A nor statement B is correct

(E) None of these

**Answer: (d)**

Explanation

Correct Option:

(D) Both statements are incorrect.

Incorrect Options:

Therefore, option (D) is correct and rest of the options is incorrect.

*play_arrow*Decimal Number System*play_arrow*Binary Number System*play_arrow*Decimal to Binary Conversion*play_arrow*Hexadecimal Number System*play_arrow*Octal Number System*play_arrow*Binary Addition

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