Question

The number system with base 16 is called
1. Binary number system
2. Octal number system
3. Hexadecimal number system
4. Decimal number system

Answer 1

Correct Answer - Option 3 : Hexadecimal number system

The correct answer is Hexadecimal number system.

• Hexadecimal numbers are used extensively in microprocessor work. 
• The hexadecimal number system has a base of 16.
• After reaching 9 in the hexadecimal system, we continue as A, B, C, D, E, F. 
• For converting a decimal number to a hexadecimal number, the number is successively divided by 16 with remainders occupying the successive positions from the right.

The procedure is exactly similar to the procedure for converting a decimal number to binary. 

For example: N = A_n Bⁿ + A_{n − 1} B^{n − 1} + . . . + A₁ B¹ + A₀ B⁰ . . .  

where, N = number, B = base, A_n = (n + 1)^th digit in that base. 

Converting hexadecimal to the decimal.

Let hexadecimal number =11

So, N = 1*161 + 1*160 = 1*16 + 1*1 =16 +1 = 17

The decimal number 11 is smaller than the hexadecimal number 11.

Decimal	Binary	Hexadecimal
0	0000	0
1	0001	1
2	0010	2
3	0011	3
4	0100	4
5	0101	5
6	0110	6
7	0111	7
8	1000	8
9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F