Problem 1 :
(a) Multiply the following 2's complement 8-bit numbers using Booth's algorithm. Show the steps as shown in Fig. 3.11.2 in Section 3.11 of the In More Depth of the COD3e CD. Verify your answer by computing A, B and the product in decimal.

Multiplicand A = 0010 1110
Multiplier B = 0100 1101

(b) Fill in the table at the end of section 3.11 that defines the the 2-bit (modified) Booth Algorithm. Repeat part (a) using this algorithm.

Problem 2 :
(a) Divide the following positive numbers using the restoring division algorithm.  Show all the steps as in Figure 3.12 on page 186 of the text book.

Verify your answer by converting A and B and your result (A / B)  and remainder to decimal.

A = 0100 1101
B = 0111

(b) Repeat using the non-restoring algorithm.  Be sure to show all steps. Note: Problem 3.29 on page 231 discusses the concept of non-restoring division.

Problem 3 :
(a) Show the IEEE 754 binary representation for the floating point number 23.6875 (base 10)
(b) Convert the following number given in IEEE 754 binary representation to the equivalent decimal number
0100 0101 0010 1000 0100 0000 0000 0000