1. The twos complement integer division algorithm discussed in class is known as the restoring method because the value in the A register must be restored following unsuccessful subtraction. A slightly more complex approach, known as nonrestoring, avoids the unnecessary subtraction and addition. Propose an algorithm for this approach.

2. Divide -145 by 13 in binary twos complement, using 12-bit words. Use the restoring method algorithm. You must show your work to receive credit for this question.

3a. Consider a fixed-point representation using decimal digits, in which the implied radix point can be in any position (to the right of the least significant digit, to the right of the most significant digit, and so on). How many decimal digits are needed to represent the approximation of both Plancks constant (6.63 * 10^-27) and Avogadros number (6.02 * 10²³)? The implied radix point must be in the same position for both numbers.

3b. Now consider a decimal floating-point format with the exponent stored in a biased representation with a bias of 50. A normalized representation is assumed. How many decimal digits are needed to represent these constants in this floating-point format?

4. Express the following numbers in IEEE 32-bit floating point format: -5; -6; -1.5; 384; 1/16; -1/32

5. The following numbers use the IEEE 32-bit floating point format. What is the equivalent decimal value?

5a. 1 10000011 11000000000000000000000

5b. 0 01111110 10100000000000000000000

5c. 0 10000000 000000000000000000000000