Please give detailed problem solving process! Thank you! Convert the numbers int

Question

Please give detailed problem solving process! Thank you!

Convert the numbers into the new base (these are signed integers) assuming that you have 8 bits to represent the number. -125_10 into base 2 and base 16 107_10 into base 2 and base 16 Convert the numbers in part B to their two's complement (same thing as multiplying by -1). Add the values from part B together (ie -127+107) using binary arithmetic. Show that -(-125+107) is equal to the two's complement of the answer in part D. Using 8 bits perform the binary equivalent of: (6 * 7), (-6 * 7), 6/7, 7/6, -6/7

Explanation / Answer

1)

-125

we need to calculate 125 in binary and then do 2's complement of the same to get the -125.

125 in binary will be 1111101. reversing the bits we get 000010 and adding 1 to the same we get 0000011.

since it is in 8 bit form the result will be 10000011

Hexadecimal will be 83.

2)

To convert 107 in binary we need to divide it by 2 and keep the reminder. so on successive division we get

1101011

Now to convert it into hex we need to make pairs of 4 so it will be 110 1011

0110 is 6 and 1011 is B

so hexadecimal value will be 6B.

C)

10000011 2's complement will be 01111100 adding 1 to it we get 01111101 which is 125.

1101011 2's complement will be 0010100 adding 1 to it we get 10010101 which is -107.

D)

adding it we get 10000011

01101101

Result will be 11110000

E)

two's complement of the number will be 00001111 +1 = 00010000

which is equivalent

F)

42 will be 00101010

-42 will be 11010110

  

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