1)[9 points]Find the eightbit2's complementary representation for the following decimal numbers:

a)121b)-121c)54

2)[3 points]Is there a relationship between EBCDIC character representation of the decimal digits from 0 to 9 and their BCD representation? Explain.

3)[5 points]Consider a hypothetical computer system. A 12-bit memory space is used for a sign-and-magnitude representation of integers with BCD and the sign is stored in MSB. What is the range of signed integers in base 10 that can be represented? Explain.

4)[18 points]Consider the two following decimal numbers: 15,675 and -8,741

a) Convert these numbers to 9's complement five-digit representation and show all the steps

b) Find the sum of the two numbers in 9's complement arithmetic showing all the steps and convert the sum back to decimal

c) Was there a carry or overflow condition in your calculation? Explain

d)Convert the initial two numbers to 10's complement representation and show all the steps

e) Find the sum of the two numbers in 10's complement arithmetic showing all the steps and convert the sum back to decimal

f) Compare the two procedures and explain the difference of addition in 9's and 10's complement. Which one is easier to implement?

5)[6 points]Provide the Packed Decimal representation of the following decimal numbers:

a)-76b)4389c)-5005

6)[6 points]What number isrepresentedin 9's complement by:

a)4987(four-digit 9^'complement representation)b) 836(three-digit 9^'complement representation)

7)[6 points]Perform the calculation 95.675 + 0.95675 using the decimalfloating pointrepresentation SEEMMMMM, where S is the sign (0 for "plus", 1 for "minus"), EE is the decimal exponent in excess-50 notation and MMMMM is the five-digit mantissa. Show all steps and explain the result.

8)[18 points]Convert the following binary numbers to floating-point format using single-precision IEEE 754 format.

Convert your answer to hexadecimal format.

a)11001.0101b)-101.111101c)-0.0101001

9)[21 points]Convert the following hexadecimal numbers to floating-point format using single-precision IEEE 754

format. Convert your answer to hexadecimal format.

a)251Db)-B26.9c)-0.00A5

10)[7 points]Convert the following decimal number to floating-point format using single-precision IEEE 754

format. Express your answer in hexadecimal format. Do the conversions with 8 bits of precision in the

mantissa.

-23.103

11)[21 points]The following numbers are in IEEE 754 single-precision floating-point format. What decimal numbers

do they represent?

a)C4C2E000₁₆b)483C5400₁₆c)BEF80000₁₆

12)[3 points]Define or explain briefly: normalization of afloating pointnumber.

13)[2 points]True or False: Double precision floating point format can store all real numbers in the range 2^-126to 2¹²⁷.

14)[1 point]True or False: In one's binary complement, negative numbers are represented by themselves.

15)[2 points]In the IEEE 754 format, the exponents 0 and 255 are used to represent special values.

16)[2 points]A number ofmagnitudetoo large to be stored in a computer is an example of what condition?

The answer form for this assignment is available on the website.