COP3502: Introduction to Computer Science Yashas Shankar Hardware

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)

Normally open switch IN OUT Control IN = 0, Control = 0  OUT = 0 IN = 0, Control = 1  OUT = 0 IN = 1, Control = 0  OUT = 0 IN = 1, Control = 1  OUT = 1 IN OUT01 CONTROL

Normally closed switch IN OUT Control IN = 0, Control = 0  OUT = 0 IN = 0, Control = 1  OUT = 0 IN = 1, Control = 0  OUT = 1 IN = 1, Control = 1  OUT = 0 IN OUT01 CONTROL

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

AND ** P AND Q are true  P is true AND Q is true ** ** Note: we use concatenation for AND ** AND PQPQ

OR ** P OR Q is true  P is true OR Q is true OR both are true** ** Note: we use + for OR ** OR PQP + Q

NOT If P is true NOT P is false If P is false NOT P is true We use ‘ for NOT PP’ 01 10

AND GATE AND PQPQ P Q PQ P Q Normally open switch

NOT GATE NOT PP’ P P’ 1 P Normally closed switch

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

Binary Arithmetic Addition Multiplication x

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)

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)

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