1What is the largest binary numberthat can be expressed with

1-What is the largest binary numberthat can be expressed with 16 bits? What are the equivalent decimal and hexadecimal numbers?

2- Convert the following binary numbers to hexadecimal and to decimal:

(a)1.10010

(b)110.010

Explain why the decimal answer in (b) is 4 times that in (a).

Solution

1. Ans) The largest number that can be represented by 16 bits is

Binary =1111 1111 1111 1111 b

Decimal=2ⁿ-1 where n = no of bits

so Decimal equivalent is 2¹⁶-1=65536-1=65535

Equivalent hexadecimal = Group each 4 bit group from binary and find equivalent hexadecimal gives

hexadecimal of whole number

   1111 1111 1111 1111

   F F F F

so equivalent hexadecimal is FFFF

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