7. Give the 32-bit floating point number (single precision) for the base ten num

Question

7. Give the 32-bit floating point number (single precision) for the base ten number -1245.2 8. Consider the Hamming Code for four bit numbers using odd parity. What is the 7-bit word (including parity bits) that should be used to describe the following integers: a, 6 9 For your answer to 2a. above, change the bit in position 3. Show how the Hamming Code is used to correct that bit. 10. For your answer to 8a. above, change the bits in position 3 and 7 a) b) Is the Hamming Code able to detect an error? Explain Is the Hamming Code able to correct the error? Explain

Explanation / Answer

According to chegg guidelines i have to solve first question only

The decimal number is -1245.2

Since number is negative sign = 1

Convert 1254.2 to binary.

1245 = 1024+128+64+16+8+4+1= 100 1101 1101

.2 = 0.0011 0011 0011 0

The binary number is 100 1101 1101.0011 0011 0011 0

It is also written as 1.0011 0111 0100 1100 1100 110 * 210

Mantissa = 0011 0111 0100 1100 1100 110

Exponent = 10 (Since 2 power value is 10)

IEEE Exponent = Exponent + Bias

Here Bias is 127 (Since IEEE 32-bit).

IEEE Exponent = 10 + 127 = 137

IEEE Exponent (Binary) = 128 + 8 + 1 = 1000 1001

IEEE 754 format 32 - bit representation:

sign

IEE Exponent

Mantissa

1

1000 1001

0011 0111 0100 1100 1100 110

sign

IEE Exponent

Mantissa

1

1000 1001

0011 0111 0100 1100 1100 110

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