Question

Show the steps of the O(n¹.59) divide-and-conquer multiplication algorithm (Section 7.1 in the textbook) for the binary numbers x = 1100 and y = 1010.

Answer 1

To use the O(n¹.59) divide-and-conquer multiplication algorithm for binary numbers x = 1100 and y = 1010, convert them to decimal, multiply the decimal numbers, convert the decimal product back to binary, and pad zeros to match the length of the original binary numbers.

Step-by-step explanation:

Step 1: Convert the binary numbers to decimal

x = 1100 = 12, y = 1010 = 10

Step 2: Multiply the decimal numbers

x * y = 12 * 10 = 120

Step 3: Convert the decimal product back to binary

120 = 1111000 in binary

Step 4: Pad zeros to match the length of the original binary numbers

Since the original binary numbers had 4 digits, we need to add 4 zeros to the left of the binary product: 00001111000