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Colt1911 [192]
3 years ago
10

Write down the bit pattern in the fraction of value 1/3 assuming a floating point format that uses Binary Coded Decimal (base 10

) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?
Computers and Technology
1 answer:
vekshin13 years ago
8 0

Answer:

The resulting floating bit representation is:

0 00101010101010101 000001                 (24 bits)

Explanation:

Converting 1/3 in decimal: 0.3333...

For converting decimal number into binary we know that the digits on the left of decimal are multiplied with positive powers of 2 (starting from zero) while digit on right side are multiplied with negative powers of  2 (starting from -1).

For example: The number 123.45 (decimal) is equal to:  

=1 * 10^2 + 2 * 10^1 + 3 * 10^0 + 4 * 10^-1 + 5 * 10^-2

=1 * 100 + 2 * 10 + 3 * 1 + 4 * 0.1 + 5 * 0.01

Now for the decimal number 0.3333... the pattern becomes:

0*0 . 3*2^-1+3^-2+3^-3+3^-4.....

The first negative power (2^-1 = 0.5) is too large to fit. The next one is 2^-2 = 0.25 and it fits, so let's subtract that: 0.3333… - 0.25 = 0.08333… The next power that fits is 2^-4 = 0.0625. Subtracting that from the remaining result we get 0.08333…- 0.0625 = 0.0208333…

Continuing on this line we get:

0.3333333…. (decimal) = 0.0101010101010101….. (binary)

Now for creating a 24 bit floating point format that uses Binary Coded Decimal we have to assign bits as follows:

  • 6 bits for the exponent
  • 17 bits for the mantissa.
  • In this case the sign bit is 0 (1 bit) because the number is non-negative.

As we need not to normalize obtained number, then the exponent will be simply 1, and the mantissa remains: 00101010101010101...

Now

The mantissa is 0.0101010101010101 (17 bits)

The exponent is 000001 (6 bits).

The resulting floating bit representation is 0 00101010101010101 000001

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Design and implement an algorithm that gets as input a list of k integer values N1, N2,..., Nk as well as a special value SUM. Y
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Answer:

Follows are the code to this question:

def FindPair(Values,SUM):#defining a method FindPair  

   found=False;#defining a boolean variable found

   for i in Values:#defining loop for check Value  

       for j in Values:#defining loop for check Value

           if (i+j ==SUM):#defining if block that check i+j=sum

               found=True;#assign value True in boolean variable

               x=i;#defining a variable x that holds i value

               y=j;#defining a variable x that holds j value

               break;#use break keyword

       if(found==True):#defining if block that checks found equal to True

           print("(",x,",",y,")");#print value

       else:#defining else block

           print("Sorry there is no such pair of values.");#print message

Values=[3,8,13,2,17,18,10];#defining a list and assign Values

SUM=20;#defining SUM variable

FindPair(Values,SUM);#calling a method FindPair

Output:

please find the attachment:

Explanation:

In the above python code a method, "FindPair" is defined, which accepts a "list and SUM" variable in its parameter, inside the method "found" a boolean variable is defined, that holds a value "false".

  • Inside the method, two for loop is defined, that holds list element value, and in if block, it checks its added value is equal to the SUM. If the condition is true, it changes the boolean variable value and defines the "x,y" variable, that holds its value.
  • In the next if the block, it checks the boolean variable value, if the condition is true, it will print the "x,y" value, otherwise, it will print a message.  

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A string that contains only 0s,1s, and 2s is called a ternary string. How many strings of 10 ternary digits (0, 1, or 2) are the
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Answer:

Number of strings = (10, 2)×(8,3) = 2520

Explanation:

The number of possible combinations for taking two 0's is C(10, 2)

It remains 8 Positions

The number of possible combinations for taking three 1's is C(8,3)

So there remains 5 spots

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