# 16 February, 2000

## The quiz

• Wednesday, 1 March
• Covers roughly Chapter 1 to Section 4.3 (don't cares)
• Closed book
• List of algebraic indentities will be provided
• Fill-in-the blank truth tables will be provided
• Fill-in-the blank Karnaugh maps will be provided
• Sources of problems
• Homework assignments
• Lab

## Sigma notation

Express boolean functions by enumerating the "on" values

``` _         _    _         _    _    _    _    _    _         _         _    _
| |    |   _|   _|  |_|  |_   |_     |  |_|  |_|  |_|  |_   |     _|  |_   |_
|_|    |  |_    _|    |   _|  |_|    |  |_|   _|  | |  |_|  |_   |_|  |_   |
```

Left upper segment can be expressed as

• F(B0,B1,B2,B3) = Σ(0,4,5,6,8,9,10,11,12,14,15)

This requires an unusual numbering of the Karnaugh map.

## Don't cares

Sometimes a particular input just doesn't matter

``` _         _    _         _    _    _    _    _                   _
| |    |   _|   _|  |_|  |_   |_     |  |_|  |_|  ???  ???  ???  |    |_|   _
|_|    |  |_    _|    |   _|  |_|    |  |_|   _|  ???  ???  ???  |_   | |
```

Best done with a Karnaugh map.

## espresso

A public domain circuit minimization tool from UC-Berkeley used in many university logic design courses.

### Input format

```.i 4
.o 1         #           Comments
.p 16        #
0000 0       #   \ CD     00      01      11      10
0001 0       #  AB\     ------------------------------
0010 1       #  00 |     0(0)    1(0)    3(1)    2(1)
0011 1       #  01 |     4(1)    5(1)    7(1)    6(1)
0100 1       #  11 |    12(0)   13(0)   15(1)   14(1)
0101 1       #  10 |     8(0)    9(0)   11(1)   10(0)
0110 1
0111 1
1000 0
1001 0
1010 0
1011 1
1100 0
1101 0
1110 1
1111 1
.e
```

```.i 4
.o 1
.p 4
01-- 1
--11 1
0-1- 1
-11- 1
.e
```