CS 1308 – Computer Literacy and the Internet

It’s Not Magic  The goal of the next series of lectures is to show you exactly how a computer works.  We will discuss the logic used to create computer instructions and how the computer decides which instructions to execute.  Although at times it may appear to be magical. It’s just math and science. 2

Our Picture of a Computer Data Bus memory input/ output control unit arithmetic- logic unit Central Processing Unit (CPU) registers

The Reliability of Binary Representation  Electronic devices are most reliable in a bistable environment  Bistable environment  Distinguishing only two electronic states  Current flowing or not  Direction of flow  Computers are bistable: hence binary representations 4

A Switch is a 2-state device that can be toggled A relay is a switch built with an electromagnet 5 controlled current controlling current when the controlling current is 1, the electromagnet pulls the switch closed, and the controlled current flows through the switch

Switches can do it all  With switches we can implement AND, OR, and NOT gates  With just those types of gates, we can design circuits to perform any computation  Remember, computers do very simple tasks, very quickly 6

Basic electric circuits: Computing AND CS Computer Fluency 7 in1 in2 out truth table for AND } when both inputs are 1, the circuit is closed and in1 in2 out = in1 in2 out power source in1 in2

Basic electric circuits: Computing OR 8 in1 in2 out truth table for OR } in1 in2 out or = in1 + in2 out in1 in2 when either input is 1, the circuit is closed

Basic electric circuits: Computing NOT 9 in1 out truth table for NOT } A new type of switch which is closed at rest in1 out = in1’ not out in1

A better switch: Transistors  bi-stable, solid state device  switching is done electronically, not mechanically  no moving parts; therefore, fast, small, reliable  can switch states in about one 10 billionth of a second  about 5 million transistors can fit on a chip 1 centimeter square. Density is increasing rapidly with new technology. 10

Figure 4.11 Simplified Model of a Transistor CS Computer Fluency 11

Boolean Logic and Gates: Boolean Logic  Boolean logic describes operations on true/false values  True/false maps easily onto bistable environment  Boolean logic operations on electronic signals may be built out of transistors and other electronic devices 12

Boolean Logic (continued)  Boolean expressions  Constructed by combining together Boolean operations  Example: (a AND b) OR ((NOT b) AND (NOT a))  Truth tables capture the output/value of a Boolean expression  A column for each input plus the output  A row for each combination of input values 13

Boolean Logic (continued)  Example: (a AND b) OR ((NOT b) and (NOT a)) 14 abValue

Building Computer Circuits: Introduction  A circuit is a collection of logic gates:  Transforms a set of binary inputs into a set of binary outputs  Values of the outputs depend only on the current values of the inputs  Combinational circuits have no cycles in them (no outputs feed back into their own inputs) 15

A Compare-for-equality Circuit  Compare-for-equality circuit  CE compares two unsigned binary integers for equality  Built by combining together 1-bit comparison circuits (1-CE)  Integers are equal if corresponding bits are equal (AND together 1-CD circuits for each pair of bits) 16

A Compare-for-equality Circuit (continued)  1-CE circuit truth table 17 abOutput

Figure 4.22 One-Bit Compare for Equality Circuit CS Computer Fluency 18

A Compare-for-equality Circuit (continued)  1-CE Boolean expression  First case: (NOT a) AND (NOT b)  Second case: a AND b  Combined: ((NOT a) AND (NOT b)) OR (a AND b) 19

Examples Of Circuit Design And Construction  Compare-for-equality circuit  Addition circuit  Both circuits can be built using the sum-of- products algorithm 20

An Addition Circuit  Addition circuit  Adds two unsigned binary integers, setting output bits and an overflow  Built from 1-bit adders (1-ADD)  Starting with rightmost bits, each pair produces  A value for that order  A carry bit for next place to the left 21

An Addition Circuit (continued)  1-ADD truth table  Input  One bit from each input integer  One carry bit (always zero for rightmost bit)  Output  One bit for output place value  One “carry” bit 22

Figure 4.24 The 1-ADD Circuit and Truth Table 23

An Addition Circuit (continued)  Building the full adder  Put rightmost bits into 1-ADD, with zero for the input carry  Send 1-ADD’s output value to output, and put its carry value as input to 1-ADD for next bits to left  Repeat process for all bits 24

Computer Instructions  The logic for every instruction is executed on every cycle by the Arithmetic and Logic Unit (ALU).  The answer used is the one for the instruction that is currently decoded and executed by the CPU.  This selection is done by the Control Circuits. 25

Control Circuits  Do not perform computations  Choose order of operations or select among data values described by the instruction  The pattern of ones and zeros in each instruction will determine the which result is used from the ALU 26

Control Circuits (cont.)  Major types of controls circuits  Multiplexors  Select one of inputs to send to output  Decoders  Sends a 1 on one output line, based on what input line indicates CS 1308 – Computer Literacy and the Internet 27

Summary  Binary values create a bistable environment, making computers reliable  Boolean logic maps easily onto electronic hardware  Circuits are constructed using Boolean expressions as an abstraction  Computational and control circuits may be built from Boolean gates 28