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## Exam 1 Notes/Cheat Sheet

by: Aubrey Putnam Graber

20

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# Exam 1 Notes/Cheat Sheet ECE 102

Aubrey Putnam Graber
CSU

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This page covers all the material that was gone over before the first midterm.
COURSE
Digital Circuit Logic
PROF.
Anura P Jayasumana
TYPE
Study Guide
PAGES
2
WORDS
CONCEPTS
Digital, Cicuit, logic
KARMA
50 ?

## Popular in Electrical Engineering

This 2 page Study Guide was uploaded by Aubrey Putnam Graber on Thursday July 28, 2016. The Study Guide belongs to ECE 102 at Colorado State University taught by Anura P Jayasumana in Summer 2016. Since its upload, it has received 20 views. For similar materials see Digital Circuit Logic in Electrical Engineering at Colorado State University.

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Date Created: 07/28/16
Digital vs. Analog Systems: In a digital system the physical quantities or signals can assume only discreet values, whereas in an analog system  the physical quantities or signals may vary continuously over a specified range. Digital Boole Positive Sign Magnitude 1's 2's Hex Systems have greater accuracy and reliability an Integers Comp. Comp. than analog systems. 0000 0 0 0 0 0 Positional Number System: 0001 1 1 1 1 1 Position of number carries value. Decimal to Binary: 0010 2 2 2 2 2 Divide decimal number by 2. ex: 327 = 0011 3 3 3 3 3 101000111. 0100 4 4 4 4 4 Convert Binary to Hex:  To Decimal:  0101 5 5 5 5 5 01110011=73H  73H (7*16)+3 = 115 Addition of Binary: Subtraction of Binary: 0110 6 6 6 6 6 0111 7 7 7 7 7 327 = 101000111 15 =1111  22 + = 010110 10 ­ =1010 1000 8 0(negative/dirty) ­7 ­8 8 349 = 101011101 5 = 0101 Multiplication of Binary:ivision of Binary: 1001 9 ­1 ­6 ­7 9 1010 10 ­2 ­5 ­6 A 23    =10111 11 * =   1011         =10111 1011 11 ­3 ­4 ­5 B         10111 1100 12 ­4 ­3 ­4 C      00000    10111 +  Subtraction of Hex: 1101 13 ­5 ­2 ­3 D 1110 14 ­6 ­1 ­2 E Addition of Hex:  471 =0100 0111 0001  3A5 ­ =0011 1010 0101 3A5 =0011 1010 0101  0CC =0000 1100 1100 1111 15 ­7 0(dirty) ­1 F 471 ­ =0100 0111 0001 816H =1000 0001 0110 ASCII: Binary to Octal: ­Pattern of binary AND GATE TRUTH TABLE (*) 10 101 101 =255 NOT GATE TRUTH numbers that TABLE  represent characters A B X like “a” and “A”. A A’ 0 0 0 ­1st bit always zero = always eight bits Unicode: 0 1 0 1 0 ­Different characters = Different Languages/symbols How Computers read music: 1 1 0 0 ­Read the values at points in a sound wave, how close you take the values the more accurate the final product0 1 1 1 ­Telephone = takes 8000/sec = 8 bit sample 1 0 ­CD = 44.1khz = 44100/sec = 16 bit sample ­90 minutes of music = 44100*16*60*90 How Computers Represent Pictures:            00H = Black, FF = White; 16 bits color OR GATE TRUTH TABLE (+) XOR GATE TRUTH TABLE (+) = 5 bits red, 5 bits blue, 6 bits green Prime Colors when you emit color = A B X Red/Blue/Green; Prime Colors when A B X you reflect color = Red/Blue/Yellow 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 THEOREMS IN BOOLEAN ALGEBRA: Operations with 0 and 1: 1. X+0  =  X 1D. X*1 = X 2. X+1 = 1 2D. X*0 = 0 Idempotent Laws: 3. X+X = X 3D. X*X = X Involution Law: 4. (X’)’ = X Laws of Complimentary: 5. X+X’ = 1 5D. X*X ’= 0 Commutative Laws: 6. X+Y = Y+X 6D.  XY = YX Associative Laws: 7. (X+Y)+Z = X+(Y+Z) 7D. (XY)Z = X(YZ) = XYZ  = X+Y+Z Distributive Laws: 8. X(Y+Z) = XY+XZ 8D. X+YZ = (X+Y)(X+Z) Simplification Theorems: 9. XY+XY’ = X 9D. (X+Y)(X+Y’) = X 10. X+XY = X 10D. X(X+Y) = X 11. (X+Y’)Y = XY 11D. XY’+Y = X+Y Theorems for Multiplying out and factoring: 12. (X+Y)(X’+Z) = XZ+XY’ 12D. XY+X’Z = (X+Z)(X’+Y) Consensus Theorem: 13. XY+YZ+X’Z = XY+X’Z 13D. (X+Y)(Y+Z)(X’+Z) = (X+Y(X’+Z) DeMorgan’s Law: 14. (X+Y+Z+…)’ = X’Y’Z’… 14D. (XYZ…)’ = X’+Y’+Z’+… Duality: 15. (X+Y+Z+…)ᴰ = XYZ… 15D. (XYZ…)ᴰ = X+Y+Z+… Sign Magnitude: The problem of representing a number's sign can be to allocate one sign bit to represent the sign:  set that bit (often the most significant bit) to 0 for a positive number, and set to 1 for a negative number. The  remaining bits in the number indicate the magnitude (or absolute value). Hence in a byte with only 7 bits (apart from  the sign bit), the magnitude can range from 0000000 (0) to 1111111 (127). Thus you can represent numbers from  −127 10o +127 10nce you add the sign bit (the eighth bit). A consequence of this representation is that there are two  ways to represent zero, 00000000 (0) and 10000000 (−0). This way, −43 10ncoded in an eight­bit byte is  10101011.This approach is directly comparable to the common way of showing a sign (placing a "+" or "−" next to the number's magnitude). One’s Compliment:  The ones' complement form of a negative binary number is the bitwise NOT applied to it — the  "complement" of its positive counterpart. Like sign­and­magnitude representation, ones' complement has two  representations of 0: 00000000 (+0) and 11111111 (−0). As an example, the ones' complement form of 00101011  (4310 becomes 11010100 (−43 ) 10 Two’s Compliment:  negative numbers are represented by the bit pattern which is one greater (in an unsigned  sense) than the ones' complement of the positive value. Hint: Start from the right, find the first 1, Invert all of the bits  to the left of that one. Ex: 0101001 = 1010111

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