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Chapter 3 Boolean Algebra and Digital logic (circuits (sequential circuits…
Chapter 3 Boolean Algebra and Digital logic
0.0 Objectives
boolean logic & digital computer circuits
design simple logic circuits
how complex computer systems works
3.1 introduction
George Boole 指出 逻辑可以用方程表示
boole's laws of thought
used in nowadays computer
boolean expressions
运算优先级
NOT> AND> OR
why: eliminate the confusion
standardized or canonical典型的 form.
product-of-sum
sum-of-product
即便不是最简化的
simplification of expressions
why： simple circuits
cheaper
less power
faster
boolean identities/law 运算法则
demorgan's law
complements
补充品，即具有相同功能的不同表达形式
why: economical using the complement function
logically equivalent exptression
gates
logic gates
universal gates
NAND, NOR
cheap to manufacture
any boolean function can constructed using only them
AND, OR, NOT, XOR,(exclusive or)
XOR is very useful in parity checkers and adders
1~6 transistors in reality, but designers think of them as a single unit
can have multiple inputs and outputs
circuits
digital circuits
digital analysis
analysisexplores the relationship between a circuits inputs and its outputs.
digitial synthesis
synthesiscreates logic diagrams using the values specified in a truth table.
embedded systems
small special-purpose computers that can execute very fast
require special programming that demands an understanding of the operation of digital circuits
integrated circuits
collections of gates for particular purpose
combinatiorial circuits
当值一输入，几乎马上就输出值 快
half adder
XOR SUM
AND CARRY
full adder
combined 2 half adders
ripple-carry adder
combined full adders
decoders
善于选取记忆存储位置
n input select any 2^n locations
一入多出
multiplexer
opposite of decoder
a select single output from several inputs depends on
control lines
n inputs, log2(n) control lines are needed
一出多入
shifter
move the bits one position to the left or right
sequential circuits
为了存储
events can be sequenced
controlled by clocks
rely on feedback, thus, output is looped back to the input
SR flip-flop
set/reset
undefined/unstable when S & R both = 1
JK flip-flop
Jack Kilby
modified from SR
D flip-flop
modified from SR
AND a clock in practice
fundamental circuit of computer memory
are used when we have a stateful(下一步取决于上一步) application
clocks
A “clock” is a special circuit that sends electrical pulses through a circuit
Clocks produce electrical waveforms
flip-flops
触发器
finite state machines
stateful application
one where the next state of the machine depends on the current state of the machine and the input.
requires both combinational and sequential logic.
register
binary counter