Assignment 4 (Assigned September 1)

For problems 1-4 below, assume 4-bit words and integers represented in 2's complement form.

1. Which of the following binary numbers are negative?
        a.) 1100                    b.) 0101                    c.) 1001

2. Negate the following numbers:
        a.) 0001                    b.) 1010                    c.) 1001

3. Give the binary representation for:
        a.) -7                        b.) -1                         c.) 7

4. Perform the following operations and indicate, in each case, whether or not overflow occurs:
        a.)    1000                b.)    1000                c.)    1111                    d.)    0000
              +0001                      +1111                      -0001                          -1111

5. An expedition to Mars found the ruins of a civilization. The explorers were able to translate the
    mathematical equations:
                5x² -50x + 125 = 0
    with the solutions:
                x = 5    and    x = 8.
    The x = 5 solution seemed okay, but x = 8 was puzzling. The explorers reflected on the way
    in which Earth's number system developed. How many fingers would you say the Martians had?

6. Suppose Venetians use a trinary number system with their three digits defined as follows:
        X    denotes    +1
        Y    denotes      0
        Z    denotes     -1

    Numbers in their system consist of four trinary digits with the value of the number B3B2B1B0 given
    by the expression: 27*B3 + 9*B2 + 3*B1 + B0. For example, XZYX = 19.

        a.) What values does ZYYX represent?

        b.) How do Venetians represent +30?
             How do they represent -30?

        c.) How many different values can Venetians represent in their system?

        d.) Suppose MAX is the largest positive integer Venetians can represent in their system. Can
             they represent all integers in the range from 0 to MAX, inclusive? What about from -MAX to
             0, inclusive?