Problem 1.8. As in Problem 1.6, suppose you have available a pocket calculator that can multiply a four-figure number by a four-figure number and get the cor- rect eight-figure answer. Devise an algorithm for multiplying two large numbers based on the classic algorithm, but using blocks of four figures at a time instead of just one. (If you like, think of it as doing your calculation in base 10000 arith- metic.) For instance, when multiplying 1234567 by 9876543, you might obtain the arrangement shown in Figure 1.11. 0123 4567 0987 6543 0080 7777 1881 0012 1851 7629 0012 1932 5406 1881 Figure 1.11. Multiplication in base 10000 Here the first line of the calculation is obtained, from right to left, as 4567 6543-2988 1881 (that is, a result of 1881 and a carry of 2988), followed by 0123x6543+2988 80777 (that is, a result of 7777 and a carry of 0080). The second line of the calculation is obtained similarly, and the final result is found by adding the columns. All the necessary arithmetic can be done with your calculator. Use your algorithm to multiply 31415975 by 8182818. Check that your answer is the same as the one you found in Problem 1.6