Attempt by: Monday, March 5
Due by: Thursday, March 8
The following problems will give you extra practice, and are strongly recommended, but you don't need to turn them in. Solutions are given on pages 693-695, but don't look at the answers until you have tried working through them on your own.
Fill out the following truth table. What can you conclude from the sixth and eighth columns of the table?
a b c a AND b a AND c (a AND b) OR (a AND c) b OR c a AND (b OR c) ------------------------------------------------------------------------------ F F F F F F F F F F T F T F F T T T F F T F T T T F T T T
Represent the following decimal (base 10) numbers in 8-bit two's complement notation. Show your work.
17 121 -67
The following numbers are written in 8-bit two's complement notation. Write their equivalents in standard decimal (base 10) notation. Show your work.
11111111 01100011 11100011
Suppose we wish to subtract three from ninety-six in binary. Show two ways to do it, one using unsigned binary numbers and traditional subtraction; the other using eight-bit two's complement and addition.
Write a simplified expression for the Boolean function defined by each of the following Karnaugh maps:
(a) \ yz
x \ 00 01 11 10
+---+---+---+---+
0 | 0 | 1 | 1 | 0 |
+---+---+---+---+
1 | 1 | 0 | 0 | 1 |
+---+---+---+---+
(b) \ yz
x \ 00 01 11 10
+---+---+---+---+
0 | 1 | 1 | 1 | 0 |
+---+---+---+---+
1 | 1 | 1 | 1 | 1 |
+---+---+---+---+
(c) \ yz
wx \ 00 01 11 10
+---+---+---+---+
00 | 1 | 1 | 0 | 1 |
+---+---+---+---+
01 | 0 | 1 | 0 | 0 |
+---+---+---+---+
11 | 1 | 1 | 0 | 0 |
+---+---+---+---+
10 | 1 | 1 | 0 | 1 |
+---+---+---+---+
Create the Karnaugh maps and then simplify for the following Boolean functions (the notation ~x means NOT x):
(a) F(x, y, z) = ~x ~y ~z + ~x y z + ~x y ~z (b) F(x, y, z) = ~y ~z + ~y z + x y ~z (c) F(w, x, y, z) = ~y z + w ~y + ~w x y + ~w ~x y ~z + w ~x y ~z
From the textbook: exercises 19 and 20, page 185. For each circuit, use the Karnaugh map technique to minimize the number of logic gates required. Show your work.
From the textbook: exercises 22, 23, and 24, page 185.