COP3502: Introduction to Computer Science

1. COP3502: Introduction to Computer Science Hardware Yashas Shankar

2. Overview of what you will learn this 2 weeks • Machine only know 0 and 1 what can we do with it, and how? • Information are represented by electrical signals • 0 usually refer to low voltage or no current • 1 usually refer to high voltage or has current • Use switches to implement hardware instructions • AND • OR • NOT • ADD • MUL • How to store 0s and 1s into a storage (memory, hard drive, etc)

3. Normally open switch IN OUT0 1 CONTROL 00 0 10 1 Control IN OUT IN = 0, Control = 0  OUT = 0 IN = 0, Control = 1  OUT = 0 IN = 1, Control = 0  OUT = 0 IN = 1, Control = 1  OUT = 1

4. Normally closed switch IN OUT0 1 CONTROL 00 1 10 0 Control IN OUT IN = 0, Control = 0  OUT = 0 IN = 0, Control = 1  OUT = 0 IN = 1, Control = 0  OUT = 1 IN = 1, Control = 1  OUT = 0

5. LOGIC • There are only 2 values • 0 (zero): usually stands for FAULT or no current • 1 (one): usually stands for TRUE or have current • Most common rules for logics • AND • Example: X and Y are even numbers • OR • X is even number or Y is even number • NOT • X is not an even number

6. AND ** P AND Q are true  P is true AND Q is true ** ** Note: we use concatenation for AND ** AND P Q PQ 1 1 1 1 0 0 0 1 0 0 0 0

7. OR ** P OR Q is true  P is true OR Q is true OR both are true** ** Note: we use + for OR ** OR P Q P + Q 1 1 1 1 0 1 0 1 1 0 0 0

8. NOT If P is true NOT P is false If P is false NOT P is true We use ‘ for NOT P P’ 0 1 1 0

9. AND GATE AND P Q PQ 1 1 1 1 0 0 0 1 0 0 0 0 P PQ Q Normally open switch Q P PQ

10. NOT GATE NOT P P’ 1 0 0 1 P P’ Normally closed switch P 1 P’

11. OR GATE OR P Q P + Q 1 1 1 1 0 1 0 1 1 0 0 0 P P + Q Q How to build an OR gate? P + Q = (P’Q’)’ ** OR gate can be built from NOT gate and AND gates **

12. Binary Arithmetic Addition + 0 1 0 0 1 1 1 10 Multiplication x 0 1 0 0 0 1 0 1

13. Building instructions from AND, OR, and NOT gates Example#1: Instruction PQ + P’Q’ (see Figure 7.6) Example#2: One-bit half adder (HA) (see Figure 7.7) Example#3: One-bit full adder (FA) (see Figure 7.8) Example#4: Four-bit full adder (see Figure 7.10)

14. Multiplexor • Multiplexor (multi-way switch) is typically used to select values or instructions • Select A or B • Select ADD or MUL • A 2-way multiplexor (Figure 7.11) • A 2-function arithmetic unit (Figure 7.12)

15. Truth table • Example#1 (P’Q’)’ • Example#2 (PQ + P’Q’) • Example#3 (P’Q + PQ’) • Example#4 (a + b)c