Question

Asked Oct 19, 2019

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

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:

2^{1} + 2^{1} + 2^{0} = (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 × 2^{0}

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 × 2^{2}

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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