A computer uses an 8-bit floating-point representation consistent with IEEE 754

Question

A computer uses an 8-bit floating-point representation consistent with IEEE 754 normalized format. It is identical to the 32-bit and 64-bit formats in terms of the meaning of fields and special encodings. The format includes 1 sign bit, 4 exponent bits, and 3 mantissa (magnitude or fraction) bits. As in IEEE 754, 0000 and 1111 in exponent field are reserved.The exponent field employs an excess-7 coding.

The following table gives the 8-bit Excess-7 representation.

Decimal

0

1

2

3

4

5

6

7

Unsigned

0000

0001

0010

0011

0100

0101

0110

0111

Excess-7

Reserved

-6

-5

-4

-3

-2

-1

0

Decimal

8

9

10

11

12

13

14

15

Unsigned

1000

1001

1010

1011

1100

1101

1110

1111

Excess-7

1

2

3

4

5

6

7

reserved

  

[Help: in normal binary representation 240 = 111100002 = 1.111 * 27 and 15.5 = 1111.12 = 1.1111 * 23]

If x = 235 (235 = 111010112), how x will be represented in this scheme? Assume, if a number cannot be represented in this scheme, the next nearest possible representation will be used.

11111111 (=155), because 238 will overflow

01101111 (= 15.5), because 238 will overflow

01110111(=240), because 235 = 1.1101011 * 27, and only 3 digits are allowed in fraction. The next nearest number with only 3 digit fraction is 1.111 * 27 =240.

01101111 (=120), because 235 = 1.1101011 * 27, and only 3 digits are allowed in fraction. The possible representation is 1.111 * 26 =224.

  

How 2.25 will be represented?

2.25 = 1.001 * 21 = 01000001

2.25 = 10.01 * 20 = 00111010

2.25 = 1.001 * 2-1 = 00110001

2.25 = 1001 * 2-2 , it cannot be represented

How -5.5 will be represented?

-5.5 = -101.1 * 20 = 11000001

-5.5 = -1.011 * 22 = 11001011

-5.5 = -1.011 * 2-2 = 00101011

-5.5 = -1011 * 2-3 , it cannot be represented

What is(are) Zero(s) in this representation?

There are no zeros

Only one zero, 00000000

Only one zero, 10000000

There are two zeroes, 00000000 and 1000000

If x = 0/0 [assume x will be NaN], which of the following will be a possible representation for x?

01111000

11111000

01111001

00001000

If x = 1/0 [assume x will be +infinity], how x will be represented?

01111000

11111000

01111001

00001000

Decimal

0

1

2

3

4

5

6

7

Unsigned

0000

0001

0010

0011

0100

0101

0110

0111

Excess-7

Reserved

-6

-5

-4

-3

-2

-1

0

Explanation / Answer

Answer:

Here, I have following solution as per given

Explanation:

The following 2.25 are represented as 2.25 = 10.01 * 20 = 00111010

Explanation:

The following -5.5 are represented as -5.5 = -101.1 * 20 = 11000001

Explanation:

The following zero(s) in this represented as Only one zero, 10000000

Explanation:

The following representation for x = 0/0 such that assume x will be NaN is 00001000

Explanation:

The following representation for x = 1/0 such that it assume x will be +infinity 00001000

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