Question

What is the mantissa and the exponent value of 6.75 is represented in 8-bit binary floating-point re?

Answer 1

Explanation:

What are the mantissa and exponent values if 6.75 is represented in 8-bit binaryfloating-point representation? a) Mantissa is 1011 and exponent is 101b) Mantissa is 0011 and exponent is 100c) Mantissa is 1011 and exponent is 100d) Mantissa is 0011 and exponent is 101.

Answer 2

In 8 bit binary floating -point representation 1011 is the mantissa and 101 is the exponent value.

Explanation:

• To represent 6.75 into binary floating-point, first we convert the decimal value to binary numbers:

            $(6)_{10}= (110)_2$

            $(0.75) \times 2= 1.50 =1\\(.50) \times 2 = 1.00 =1\\(.00) \times 2= 0$

            $0.75=(11)_2$

• after converting value is: $(6.75)_{10} = (110.11)_2 = (110.11)_2 * 20$

• collecting all the binary value:

               $(110.11)_2 \times 20 = (11.011)_2 \times 21 \\\\ (11.011)_2 \times 21 = (1.1011)_2 \times 22$

Finding Mantissa and exponent

• Mantissa value located after a decimal point, that is = 1011
• Exponent value is adds 3 after the power value,  which is equal to 3+2 = 5, after convert value into binary it will give 101 so, Exponent value is 101.  

Learn more:

• Find mantissa: https://brainly.in/question/10722200