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I\'m not sure how to do this. Please explain so I can understand. Floating point

ID: 3785011 • Letter: I

Question

I'm not sure how to do this. Please explain so I can understand.

Floating point operations Use decimal (base-10) values (2.851 times 10^1 and -9.854 times 10^-1) to illustrate the floating-point addition algorithm step by step. List the name/action of each step, and illustrate the step using the given value. Your result should have 4 significant digits. (Note: significant points refer to all meaningful digits, not the digits after decimal points. For example. 2.851 has 4 significant digits.) Use the same value as (a) to illustrate the floating-point multiplication algorithm step by step. Again, the result should have 4 significant digits. Using binary values -1.11110011 times 2^-3 and 1.10001111 times 2^2 to illustrate the floating-point multiplication algorithm step by step. Leave the result format as the input data.

Explanation / Answer

a). Add the following two decimal numbers in scientific notation:

2.851 × 101 with -9.854 × 10-1

b.) Multiply the following two numbers:

2.851 × 101 = 285.10 × 10-1

285.10 + (-9.854) = 275.246 and write the sum 275.246 × 10-1

275.246 × 10-1 = 2.75246 × 101 (shift mantissa, adjust exponent)

check for overflow/underflow of the exponent after normalisation

If the mantissa does not fit in the space reserved for it, it has to be rounded off.

2.75246 × 101===> 2.752 × 102

2.851 × 101 and -9.854 × 10-1

c.)

New Exponent = 1 + (-1) = 0

2.851 × (-9.854) = -28.093754

Can only keep three digits to the right of the decimal point, so the result is

-28.094 × 100

-2.809 × 101

-2.809 × 101

(-3 + 127) + (2 + 127) = (-1 + 127) == 126

Adjust the sign. -1.22222246 × 2-1

                1.10001111             ×  1.11110011                     ---------------                1.22222246  
The product is 1.22222246 × 2-1
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