1 Consider the following two floating point numbers coded in

1. Consider the following two floating point numbers coded in the 10-bit format defined in class:

x = 1 1010 01101 and y = 1 1001 10110

Do the following:

(a) carry out the addition, x + y, in binary. Show all of the steps of your work, displayed carefully. Make sure your final binary answer is correctly normalized. Convert the result to normalized 10-bit floating point.
(b) convert both of the numbers, x and y, to decimal form and add the numbers.
(c) convert your answer from part (a) to decimal form and compare it with part (b).

2. The bit pattern in a sequence of 4-bytes translates into AB7CF000₁₆. Assuming that this represents the bits of the number stored in these bytes in the order indicated (from left to right along all 8 hexadecimal digits), compute the decimal equivalent of the number stored here if the number is stored in

(a) Unsigned binary form
(b) Twos-complement binary form
(c) signed magnitude form
(d) IEEE-754 single precision floating point form

3. Carry out the following arithmetic operations in binary using 8421 BCD coding. Verify your results by converting the answers back to decimal form and comparing them with the results of decimal arithmetic with your calculator.

3895.84 + 7523.07

Solution

1)

X = 1101001101

Y= 1100110110

Z= 011010000011

Z=normalized form= (-1)⁰ * 10^{1110 - 111} * 1.11111 = (-1)⁰ * 2⁷ * 1.96875

b)

1 1010 01101 = 845

1 1001 10110=822

sum = 845 + 822 = 1667

c) Both the answers are same