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Which of the following statement(s) is/are TRUE ? S1 : The decimal number 11 is larger than the hexadecimal number 11. S2 : In the binary number 1110.101, the fractional part has the decimal value as 0.625.

Which of the following statement(s) is/are TRUE ? S1 : The decimal number 11 is larger than the hexadecimal number 11. S2 : In the binary number 1110.101, the fractional part has the decimal value as 0.625. Correct Answer S2 only

Binary System

  • The microprocessor operates in binary digits 0 and 1, also known as bits.
  • These digits are represented in terms of electrical voltages in the machine, generally, 0 representing a low voltage level, and 1 representing a high voltage level.
  • Each microprocessor recognizes and processes a group of bits, called the word, and microprocessors are classified according to their word length. The binary number system uses 2 as a base.

For example: N = bn qn… b3 q3 + b2 q2 + b1 q1 + b0 q0 + b-1 q-1 + b-2 q-2… etc.

11= 1x23 + 0x22 + 1x21 + 1x20 

    =    8    +  0    +    2    +    1

So, 11 as Binary will be 1011

Hexadecimal

  • Hexadecimal numbers are used extensively in microprocessor work. They are much shorter than binary numbers.
  • This makes it easy to write and remember. The hexadecimal number system has a base of 16.
  • Although any 16 digits may be used, everyone uses 0 to 9 and A to F, after reaching 9 in the hexadecimal system, one can 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 = An Bn + An − 1 Bn − 1 + . . . + A1 B1 + A0 B0 . . . 

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

Converting hexadecimal to the decimal.

Let hexadecimal number be11

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
Converting  binary to decimal fraction

​N = bn qn… b3 q3 + b2 q2 + b1 q1 + b0 q0 + b-1 q-1 + b-2 q-2… etc.

0.101= 1*2-1 + 0*2-2 + 1*2-3

            =       1/2   +   0    +   1/8

          =        0.5  +   0    +   0.125   

          =         0.625  

So, we conclude that only S2 is true and S2 is false.​

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