Question

1. (3 pts) Consider an unsigned fixed point decimal (Base10) representation with 8 digits, 5 to the left of the decimal point and 3 to the right.

a.      What is the range of the expressible numbers?

  

b.      What is the precision?

  

c.       What is the error?

  

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2. (3 pts) Convert this unsigned base 2 number, 1001 10112, to each base given below  

(Note: the space in the binary string is purely for visual convenience)

Show your work.

1. Using the Polynomial method convert the number above from base 2 to base 10 (decimal)

  

2. Using the grouping method convert number above from base 2 to base 16… (hex)  

  

3. Using the grouping method convert number above from base 2 to base 8… (octal)  

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3. (3 pts) Convert this unsigned base 2 number, 11011.100112, to each base given below  

(Note: The placement of the decimal point. Correct padding must be used)

Show your work.

1. Using the grouping method convert number above from base 2 to base 16… (hex)  

2. Using the grouping method convert number above from base 2 to base 8… (octal)  

3. Using the grouping method convert number above from base 2 to base 4… ( )  

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4. (3 pts) Convert 597.2210 (decimal number) to unsigned binary using the remainder and multiplication methods:. Stop at the 6th digit to the right of the decimal place.  (Show your work)

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5. (3 pt) Using the overflow concept and its identifying methods introduced in the class, solve the problem: suppose that we have a computing device that has only 8 bits. Using this device, add the following two unsigned 8 bit binary numbers and give the final result. If there is an overflow, point that out (you must clearly indicate whether your final result has overflow).  

                                   carry bits

      0 1 1 0   1 1 1 0

+    1 1 1 0   1 0 1 1  

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Answer:    

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6. (3 pts) Convert -12310 to an 8-bit binary number using the representations given below.   

Show all 8 bits.

1. signed magnitude number  

Answer:  

2. one's complement number  

Answer:  

3. two's complement number  

Answer:  

4. excess 128 number (bias the two’s complement number)

Answer:  

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7. (5 pts) Consider the bit pattern 1101 10102.  Provide the equivalent value in Base10 (decimal) for this bit pattern based on the following assumptions: (if the bit pattern represents a negative number under the assumed context, then give its negative value).  (show your work)

Assume the original number is expressed using:

1. signed magnitude representation  

Answer:

  

2. unsigned representation  

Answer:

  

3. one's complement representation  

Answer:

  

4. two's complement representation  

Answer:

  

  

5. excess 128 representation (biased two’s complement number)

Answer:

  

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Answer 1

Answer

1001 1011

=(1* 2⁰)+(1*2¹)+(0*2²)+(1*2³)+(1*2⁴)+(0*2⁵)+(0*2⁶)+(1*2⁷)

=1+2+0+8+16+0+0+128

=1+2+8+16+128

=155

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b)

1001 1011

1001-9

1011-B

1001 1011 = 9 B

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c)

010 011 011

010-2

011-3

011-3

010 011 011

= (233)₈

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answered one part, please post remaining question, really sorry for that

all the best