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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 - PowerPoint PPT Presentation
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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 = 0IN = 0, Control = 1 OUT = 0IN = 1, Control = 0 OUT = 0IN = 1, Control = 1 OUT = 1
INOUT 0 1
CONTROL 0 0 01 0 1
Normally closed switch
IN OUTControl
IN = 0, Control = 0 OUT = 0IN = 0, Control = 1 OUT = 0IN = 1, Control = 0 OUT = 1IN = 1, Control = 1 OUT = 0
INOUT 0 1
CONTROL 0 0 11 0 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 **
ANDP Q PQ1 1 11 0 00 1 00 0 0
OR
** P OR Q is true P is true OR Q is true OR both are true**** Note: we use + for OR **
ORP Q P + Q1 1 11 0 10 1 10 0 0
NOTIf P is true NOT P is falseIf P is false NOT P is trueWe use ‘ for NOTP P’0 11 0
AND GATE
ANDP Q PQ1 1 11 0 00 1 00 0 0
P
QPQ
P PQ
Q
Normally open switch
NOT GATE
NOTP P’1 00 1
P P’
1 P’P
Normally closed switch
OR GATE
ORP Q P + Q1 1 11 0 10 1 10 0 0
P
QP + 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
10 0 11 1 10
Multiplicationx 0 10 0 01 0 1
Building instructions from AND, OR, and NOT gatesExample#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