Question

QUESTION 3:

(No, handwritten answers pls).

QUESTION 3.1:

Convert the following number to a floating point format i.e. (SEEMMMMM) format.

73.8224

QUESTION 3.2:

Add the floating point (SEEMMMMM) number converted in Part 1 with the following number: 05564373

Answer 1

Answer 3.1:

The given Floating-point format of 8- bit word is SEEMMMMM, it has 7 decimal digit and a sign.

Here,

The first bit S is the sign bit. It is a sign of mantissa. 0 is used to represents + sign and 5 is used to represents – sign.

The given value is 73.8224 is positive.

So, The sign of the value is +.

Hence, The Value of S = 0.

Next two-bit EE is used to represents an exponent

Normalizing the value to get an exponent.

Put the decimal point at the beginning of the value.

0.738224 * 10²

The base of the exponent is 10.

The magnitude of the exponent is +2.

The default Bias (Excess) is 50

Add magnitude of the exponent 2 with bias 50

Hence, EE = 50 + 2 =52

Next, five-bit is used to represent the mantissa. MMMMM is the 5-digit Mantissa

Mantissa or magnitude is 738224.

738224 has six digits but given mantissa only hold five so write the first 5 digits.

Hence, MMMMM is 73822

Representation of Floating-point value 73.8224 into the Floating-point format SEEMMMMM is

The floating-point value in SEEMMMMM format is 05273822.

Answer 3.2:

The floating-point value of 73.8224 in the SEEMMMMM format is 05273822.

The given value in the SEEMMMMM format is 05564373.

Addition of both the values is:

First convert the number into real number

05273822 = 0.73822 * 10² = 73.822

05564373 = 0.64373 * 10⁵ = 64373

Add 73.822 with 64373

73.822 + 64373 = 64446.822

Now convert it into SEEMMMMM format

64446.822 = 0.64446822 * 10⁵

S = 0

EE = 55

MMMMM = 64446

Hence, 05564446

Addition of 05273822 and 05564373 is 05564446.