Question

# If the IEEE Standard 754 representation of a floating point number is given as 01101110110011010100000000000000, determine...

If the IEEE Standard 754 representation of a floating point number is given as 01101110110011010100000000000000, determine the binary value represented by this 32-bit number

#### Homework Answers

Answer #1

1. Identify the elements that make up the binary representation of the number:

First bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

The next 8 bits contain the exponent:
1101 1101

The last 23 bits contain the mantissa:
100 1101 0100 0000 0000 0000

2. Convert the exponent from binary (base 2) to decimal (base 10):

The exponent is allways a positive integer.

1101 1101(2) =

1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20 =

128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = 221(10)

3. Adjust the exponent:

Exponent adjusted = 221 - 127 = 94

4. put all the values into expression

(sign) (1 . Mantissa) × 2(Exponent adjusted) =

(0) (1 . 100 1101 0100 0000 0000 0000) × 294

011001101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000

if you have any doubt, feel free to ask in the comments.

Know the answer?
Your Answer:

#### Post as a guest

Your Name:

What's your source?

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Not the answer you're looking for?
Ask your own homework help question
ADVERTISEMENT
##### Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

ADVERTISEMENT