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Logic and Computing Devices Cheat Sheet (DRAFT) by

Jack Bjelland - ECE 2010

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Common Conver­sions

210
103
Kilo
220
106
Mega
230
109
Giga
240
1012
Tera

Inform­ation Display

K
103 bytes
Kib, KB (i=inf­orm­ation)
210 bytes

Number Formulas

Max value repres­ented by an n bit number
2n-1
Max value in range of fractions
(2n-1)/2n
n number of bits to represent number x
log(x)/log(2)
Digits to store n in binary
log(n)/log(2)
Digits to store b bit binary number in BCD
4x[log(2b)] <-b­rackets are rounded up

Comple­ments

(r-1)'s Complement of n, where d = number of digits
(rd-1)-n
1's Complement
Complement each bit
2's Complement
Start from right until 1. Then, take comple­ment.
For base R, R's complement of n
rd-n

Signed Arithmetic

If the value is negative, take the 2's comple­ment. Then, add both values together.

Sampling temps from -x to y. n bits per sample

y--x = Z
log(Z)/log(n) = F
Then use F as a base to find "­bin­ary­" value

Boolean Algebra Rules

X+1=1
Annulment
X+0=0
Identity
X*1=X
Identity
X*0=0
Annulment
X+X=X
Idempotent
X*X=X
Idempotent
(X')' = X
Double Negation
X+X' = 1
Complement
X*X'=0
Complement
X+Y=Y+X
Commut­ative
XY=YX
Commut­ative
X'+X' = X'X'
deMorgan's Theorem
X'X' = X'+X'
deMorgan's Theorem
X+XY = X
Absorption
X(X+Y) = X
Absorption
Associ­ative Law
Distri­butive Law
Can think of AND as series, and OR as parallel
  

Cost Criteria

litera­ls+­non­-single terms + unique comple­mented literals
Ex: ABCD+A­'B'C'D'
(8) + (2) + (4) = 14

Flip Flop Charac­ter­istic Tables

Sequential Analysis

Write all of the inputs for each flip-flop. Make a state table.

State Reduction

If two states have the same inputs and outputs, you can remove one. Remember to change the variable if it appears elsewhere.

Counters

Synchr­onous Counters
have a common clock
Ring counter
circular shift register

Types of PLD's

No fishbones, 4x16 decoder
16x8 ROM
Fishbones, x's
PLA (Progr­ammable Logic Array)
No fishbones, 2x4 decoder
4x2 ROM
Fixed ORs, same inputs
PAL (Progr­ammable Array Logic)
When finding terms, if X on 1, NOT all terms
Else, find terms normally

Parity

EVEN Function
generates ODD parity
ODD Function
generates EVEN parity