  # what are the mantissa and exponent values if 6.75 is represented in 8-bit binary floating point representation?

Question

what are the mantissa and exponent values if 6.75 is represented in 8-bit binary floating point representation?

check_circleExpert Solution

Conversion of decimal to 8-bit floating point representation:

Step 1: Convert the integer part of the decimal value to binary value.

• 6(10) = 110(2)

Step 2: Convert the fractional part of decimal value to binary value.

• 75*2 = 1.50; here, get the integer part “1” and continue with fractional part.
• 5*2 = 1.0; here, get the integer part “1” and stop. Since, nothing remains in fractional part.
• Thus, 0.75(10) = 0.11(2)

Step 3: Write the whole decimal value as binary value.

• 75(10) = 110.11(2)

Step 4: Add an exponential part.

• 11(2) = 110.11(2) * 20

Step 5: Normalize the value.

• 11(2) * 20 = 1.1011 * 2442

Step 6: Get mantissa.

• The fractional part in the normalized value is the mantissa.
• Thus, “1011” is the mantissa.

Step 7: Compute exponent.

• Add “3” to the power value.
• 3+2 is 5 and is “101”...

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