a) What is the smallest positive floating point (or real) number that is represe

Question

a) What is the smallest positive floating point (or real) number that is representable using the 12-bits on this computer. b) Find the value of the 12-bits required to represent the signed integer: -105 on this computer. c) Find the value of the 12-bits required to represent the floating point number on this computer. d) Is the number stored in Question 1(c) exact? If not what is the actual number stored? e) How many bits are required to store the three characters: Dog using the encoding in Table f) Find the actual bit pattern required to store the three characters below. Dog The remaining parts of Question 20g-refer to the following 24-bits: 2) Represent these 24-bits as a hexadecimal number ) What characters according to Table 1 are represented by these 24-bits? What pair of signed integers is represented by these 24-bits? What pair of floating point numbers could be represented by these 24-bits?

Explanation / Answer

Solution:

The first four subparts have been answered as per Chegg guidelines, please repost others.

The pair of floating point numbers which can be represented is

0101 0011 1111

and the next number will be

1101 0111 1101

b)

Solution:

The format is

sign

Exponent

Mantissa

1 bit

5 bits

6 bits

-105

105 in binary is 1101001

In normalized form

1.101001 * 2^6

Exponent= bias + actual exponent=> 15 + 6= 21, in binary=> 10101

sign

Exponent

Mantissa

1

10101

101001

c)

11.11

11.11 in binary is 1011.00011100001010001111

in normalized form

1.01100011100001010001111 * 2^3

expontnt= 15 + 3= 18=> 10010

Representation:

sign

Exponent

Mantissa

1

10010

011000

d)

Since the exponent part after normalization contains so many bits that mantissa field can't hold that is why there is an overflow of bits, and this system is not enough to represent 11.11.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

sign

Exponent

Mantissa

1 bit

5 bits

6 bits

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