  # What is the mantisa and exponent value if 6.75 represnt in 8 bit binary floating point

Question

What is the mantisa and exponent value if 6.75 represnt in 8 bit binary floating point

check_circleExpert Solution
Step 1

The mantissa and exponent value of 6.75 can be obtained by converting the given decimal number into 8-bit binary floating-point representation.

• The integer part of number i.e. 6 is converted into binary first as shown below:

21 + 21 + 20 = (110)2

• The decimal part of the given number i.e. 0.75 is converted into binary as shown below:

0.75 × 2 = 1.5 ; Generates 1 and continue with the rest

0.5 × 2 = 1 ; Generates 1 and nothing continues further.

0.75 becomes (11)2

• 6.75 becomes (110.11)2
Step 2

In the next step, exponent part is added to the generated number, so that it does not make any change in the number.

110.11 × 20

The number is then normalized in such a way that binary point is one bit from the left and the exponent value is adjusted accordingly.

1.1011 × 22

Step 3
• The fractional part of the number is considered as mantissa part. Therefore, mantissa is 1011.
• To get the exponent part, a bias is added to the exponent of two (which is 2)...

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