Computer Science 101

1. Computer Science 101 Logic Gates and Simple Circuits

2. Collector Base Switch Emitter Transistor - Electronic Switch • Base High (+5v or 1) Makes connection • Base Low (0v or 0) Disconnects • Say, 500 million transistors on a chip 1 cm2 • Change states in billionth of sec • Solid state

3. Moore’s Law In 1965, Intel co-founder Gordon Moore saw the future. His prediction, now popularly known as Moore's Law, states that the number of transistors on a chip doubles about every two years.

4. Gates • A gateis an electronic device that takes 0/1 inputs and produces a 0/1 result.

5. NOT Gate _ A A NOT Gate • Input High (+5v or 1) Output Low (0v or 0) • Input Low (0v or 0) Output High (+5v or 1) • Output is opposite of Input +5v Output Input Ground

6. Input-1 Input-2 AND Gate A B AB AND Gate • Output is 1 only if • Input-1 is 1 and • Input-2 is 1 • Output = Input1 AND Input2 +5v Output

7. +5v A B Output OR Gate A B A + B OR Gate • Output is 1 if • A is 1 or if • B is 1 • Output = A OR B

8. Boolean Expression  Python • Logical operators • AND  and (Python) • OR  or (Python) • NOT  not (Python) • NOT ((x>y) AND ((x=5) OR (y=3)) • not((x>y) and ((x==5)or(y==3))) • while (not((x>y) and ((x==5)or(y==3)))) :…

9. Abstraction • In computer science, the term abstraction refers to the practice of defining and using objects or systems based on the high level functions they provide. • We suppress the fine details of how these functions are carried out or implemented. • In this way, we are able to focus on the big picture. • If the implementation changes, our high level work is not affected.

10. Abstraction Examples • Boolean algebra - we can work with the Boolean expressions knowing only the properties or laws - we do not need to know the details of what the variables represent. • Gates - we can work with the logic gates knowing only their function (output is 1 only if inputs are …). Don’t have to know how gate is constructed from transistors.

11. Boolean Exp  Logic Circuit • To draw a circuit from a Boolean expression: • From the left, make an input line for each variable. • Next, put a NOT gate in for each variable that appears negated in the expression. • Still working from left to right, build up circuits for the subexpressions, from simple to complex.

12. Logic Circuit: _ ____ AB+(A+B)B Input Lines for Variables A B

13. Logic Circuit: _ ____ AB+(A+B)B NOT Gate for B A B _ B

14. Logic Circuit: _ ____ AB+(A+B)B _ Subexpression AB _ AB A B _ B

15. Logic Circuit: _ ____ AB+(A+B)B Subexpression A+B _ AB A A+B B _ B

16. Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression A+B _ AB A ____ A+B A+B B _ B

17. Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression (A+B)B _ AB A ____ A+B A+B B _ B ____ (A+B)B

18. _ AB A ____ A+B A+B B _ B ____ (A+B)B Logic Circuit: _ ____ AB+(A+B)B Entire Expression

19. Logic Circuit  Boolean Exp • In the opposite direction, given a logic circuit, we can write a Boolean expression for the circuit. • First we label each input line as a variable. • Then we move from the inputs labeling the outputs from the gates. • As soon as the input lines to a gate are labeled, we can label the output line. • The label on the circuit output is the result.

20. A _ AB _ A ______ _ _ AB+AB B _ AB _ B A+B ______ _ _ (AB+AB)(A+B) Entire Expression Logic Circuit  Boolean Exp _ _ AB+AB

21. Simplification Revisited • Once we have the BE for the circuit, perhaps we can simplify.

22. Logic Circuit  Boolean Exp Reduces to:

23. The Boolean Triangle Boolean Expression Logic Circuit Truth Table

24. The Boolean Triangle Boolean Expression Logic Circuit Truth Table

25. If we only had an Al Gore Rhythm!