Dr. Cynthia Furse University of Utah Introduction to Electrical & Computer Engineering Digital Circuits – Very Brief Introduction Dr. Cynthia Furse University of Utah

Digital Circuits – Brief Intro Analog & Digital Binary (Digital) Numbers & Binary Math Computers & Binary Digital Logic Gates NOT OR XOR AND NAND Hooking up Digital Circuits

Digital vs. Analog Digital is fixed (can take one or a few values, something you can count) Analog varies (can take any value, something you can measure)

Analog vs. Digital – Fuel Gauge Analog Gauge tells you ‘how much’ fuel you have Digital Light tells you you have enough (off) or you don’t (on)

Analog vs. Digital – Clocks Analog Clock tells you ‘what time it is’ (continuous) Digital clock tells you what hour and minute it is (countable)

Dr. Thomas Stockham University of Utah Analog opera recordings have distortion Digital Recording lets you remove distortion

Analog vs. Digital – Voltmeters Analog Voltmeter tells you ‘what voltage it is’ (continuous) Digital voltmeter tells you voltage to xx.xx digits (countable) OR just ‘on’ and ‘off’

Analog vs. Digital – Voltages Analog Voltage can be ‘any value’ (Dimmer Switch) Digital voltage is a limited set of voltages On =1 OR Off = 0

Analog vs. Digital – Voltages Analog Voltage can be ‘any value’ Digital voltage is a limited set of voltages (Stairstepped)

Digital – Represent with Binary #s

Analog to Digital Conversion (ADC) Digital to Analog Conversion (DAC) Analog Voltage can be ‘any value’ Digital voltage is a limited set of voltages – Quantization Error

Counting with Binary #s 000 = 0 001 = 1 010 = 2 011 = 3 100 = 4 101 = 5 110 = 6 111 = 7

Bits & Bytes 0000 0000 << 8 BITS = 1 Byte

Computer Numbers Computers represent numbers as a set of bits (8,16,32 bit) & an exponent 2000 = 2 x 10^3 00000010 = 2 00000011 = 3

Computers Represent Letters with ASCII codes A = 0100 0001 = ‘41’ a = 0110 0001 = ‘61’ B = 0100 0010 = ‘42’ b = 0110 0010 = ‘62’ C = 0100 0011 = ‘43’ c = 0110 0011 = ‘63’ D = 0100 0100 = ‘44’ d = 0110 0100 = ‘64’ Etc.

Write your name in ASCII 00000001 I 00001001 R 00010010 B 00000010 J 00001010 S 00010011 C 00000011 K 00001011 T 00010100 D 00000100 L 00001100 U 00010101 E 00000101 M 00001101 V 00010110 F 00000110 N 00001110 W 00010111 G 00000111 O 00001111 X 00011001 H 00001000 P 00010000 Y 00011010   Q 00010001 Z

How Computers Represent Pictures Pixel (eg. DPI = Dots per inch) Digital (pixels) Analog (? Or just more pixels)

How Computers Represent Pictures Color: Red + Green + Blue (RGB) Wikipedia

Computer Logic: 5V = ‘1’ = ‘on’ = ‘yes’ = ‘true’ 0V = ‘0’ = ‘Off’ = ‘no’ = ‘false’

Example: Battery Voltage Sensing A battery is considered low when its voltage is under 1.3V Battery 1 Battery 2

Example: Is the Battery Charged? ECE-speak: Is the battery voltage above 1.3V? Convert voltage to digital (0 or 5) Battery voltage Vb =5V = A(Vb-1.3V) 1.3V 0V =5V = ‘1’ 0V = ‘0’

Example: Are BOTH Batteries Charged? Are Vo1 AND Vo2 both ‘1’? AND

Example: Is at least one of the Batteries Charged? Is either Vo1 OR Vo2 ‘1’? OR

Example: Does at least one of the batteries need to be charged? Is at least one of Vo1 AND Vo2 ‘0’? NAND

Others Excusive-OR (XOR) NOT

Building with Logic Gates AND GND Remember the Power Supply Voltages! 5V

Digital Circuits – Brief Intro Analog & Digital Binary (Digital) Numbers & Binary Math Computers & Digital Digital Logic Gates NOT OR XOR AND NAND Hooking up Digital Circuits

Tombstone Rock near Moab, Utah