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27 - Floating Point Arithmetic (+ and - numbers)

 1. In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation. Read the excerpt below to fill in the blanks. 
Floating-point computation is often found in systems
 which include ____________________________________, 
which require fast processing times.

  binary and hexadecimal numbers

  None of the above

  two's complement numbers

  very small numbers and very large real numbers

 2. Over the years, a variety of floating-point representations have been used in computers. However, since the 1990s, the most commonly encountered representation is that defined by the IEEE 754 Standard

  TRUE

  FALSE

 3. A simple method to add floating-point numbers is to first represent them with the same exponent. What is happening in this example? 
 123456.7 = 1.234567 × 10^5
 101.7654 = 1.017654 × 10^2 = 0.001017654 × 10^5

  the second number is shifted right by three digits, and then the usual addition method is used

  None of the above

  the second number is shifted left by two digits and then the usual addition method is used

  the first number is shifted left by three digits and then the usual addition is used

 4. To add two floating point numbers, the ___________needs to be aligned before normal binary addition takes place.

  zeros

  exponents

  ones

  binary point

 5. In the example below, what is happening at point 1 and 2?
kevindrummexample.png

  1. Add the expnents together 2. Add the mantissa's together

  1. Making the exponents the same 2. Add the mantissa's together

  None of the above

  1. Add the mantissa's to the exponents 2. Add the exponents

 6. Performing the following addition would give the answer: 0.11001111 011
binarypointaddition.png

  TRUE

  FALSE

 7. What is the result of this addition? 
This is an example of adding with a negative exponent
binarypointaddition2.png

  The answer is 0.10010 000

  The answer is 0.11011 011

  The answer is 0.10010 001

  The answer is 0.11110 101

 8. What is the result of this binary point subtraction?
binarypointsubtraction.png

  The answer is 1.01100 111

  The answer is 1.01100 010

  The answer is 1.11101 011

  The answer is 1.00111 000

 9. In floating point addition it is important to determine which exponent is the smaller. Rewrite that number using the larger exponent, so that the two exponents are now the same.

  FALSE

  TRUE

 10. It is important to be careful when adding numbers with very different exponents since significant error can be introduced.

  TRUE

  FALSE

 11. Fortunately, two things that can never occur when performing floating point binary addition is the problem of overflow and underflow.

  FALSE

  TRUE

 12. In the above example, ‘a’ and ‘b’ are two fixed point inputs and 'c’ is the output of addition of a and b. Since both the inputs are positive therefore output of a and b is ____________ 
Example:When both a and b are positive
a=2.1=00000000000000010000110011001100
b=3.5 =00000000000000011100000000000000
c=a+b=5.6=000000000000001011001100110011000

  positive

  negative

  likely to result in an error (overflow)

  neutral

 13. Here a and b are negative numbers, so addition of two negative numbers is always _____________ 
Example : When both a and b are negative
a=-2.1=10000000000000010000110011001100
b=-3.5 =10000000000000011100000000000000
c=a+b=-5.6=10000000000000101100110011001100

  neutral

  positive

  negative

  likely to result in an error (overflow)

 14. Here a and b are negative numbers, so subtraction of of two negative numbers is always ____________________ 
Example: When both a and b are negative
a=-27.8=10000000000011011110011001100110
b=-19.6 =10000000000010011100110011001100
c=a-b=-8.2=10000000000001000100001101001111

  negative

  likely to result in an error (overflow)

  neutral

  positive

 15. ‘a’ and ‘b’ are two fixed point inputs and ‘c’ is the output of subtraction of a and b. Since both the inputs are positive therefore output of a and b is ___________ 
Example (subtraction): When both a and b are positive
a=27.8=00000000000011011110011001100110
b=19.6 =00000000000010011100110011001100
c=a-b=8.2=00000000000001000100001101001111

  positive

  neutral

  negative

  likely to result in an error (overflow)


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