Write down the bit pattern in the fraction of value 16 assum

Write down the bit pattern in the fraction of value 1/6 assuming a floating point format that uses binary numbers in the fraction. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?

Solution

In 24 bit repreentation 1st bit is sign next 8 bits are exponent and next 15 bits are Mantissa

hence 0.1666 is the decimal value

0.1666*2=0.3332

0.3332*2=0.6664

0.6664*2=1.3328

0.3328*2=0.6656

0.6656*2=1.3312

0.3312*2=0.6624

0.6624*2=1.3248

0.3248*2=0.6496

0.6496*2=1.2992

0.2992*2=0.5984

0.5984*2=1.1968

0.1968*2=0.3936

0.3936*2=0.7872

0.7872*2=1.5744

0.5744*2=1.1488

0 00000000. 001010101010011