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