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COP3502: Introduction to Computer Science. Hardware. Yashas Shankar. 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

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## COP3502: Introduction to Computer Science

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**COP3502: Introduction to Computer Science**Hardware Yashas Shankar**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 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**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**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 P Q PQ 1 1 1 1 0 0 0 1 0 0 0 0**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**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**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**NOT GATE**NOT P P’ 1 0 0 1 P P’ Normally closed switch P 1 P’**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 ****Binary Arithmetic**Addition + 0 1 0 0 1 1 1 10 Multiplication x 0 1 0 0 0 1 0 1**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

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