7C h a p t e r L o g ic C ir c u it s

1. State the advantages of digital technology compared to analog technology.

2. Understand the terminology of digital circuits.

3. Convert numbers between decimal, binary, and

other forms.

5. Understand the binary arithmetic operations used in computers and other digital systems.

6. Interconnect logic gates of various types to implement a given logic function.

7. Use Karnaugh maps to minimize the number of gates needed to implement a logic function.

8. Understand how gates are connected together to form flip-flops and registers.

A d v a n t a g e s o f t h e D ig it a l A p p r o a c h

Provided that the noise amplitude is not too large, the logic values represented by a digital signal can still be determined after noise is added.

With modern IC technology, it is possible to manufacture exceedingly complex digital circuits economically containing 10s of millions of transistors.

Definitions

P o s it iv e v e r s u s N e g a t iv eL o g ic

D ig it a l W o r d s

In p a r a lle l t r a n s m is s io n , an n-bit word is transferred on n wires, one wire for each bit, plus a common or ground wire. In

s e r ia l t r a n s m is s io n , the successive bits of the word are transferred one after the other with a single pair of wires.

B in a r y N u m b e r s

101210 1021031041072.743 −×+×+×+×=

1010123

2 5.1321212021271.1101 =×+×+×+×+×= −

G r a y C o d e

C o m p le m e n tA r it h m e t ic

The ’ o n e s c o m p le m e n t of a binary number is obtained by replacing 1s by 0s, and vice versa.

0100110110110010 (one’s complement)

The ’ t w o s c o m p le m e n t of a binary number is obtained by adding 1 to the one’s complement, neglecting the carry (if any) out of the most significant bit.

Complements are useful for representing negative numbers and performing subtraction in computers.

S u b t r a c t io n U s in g’ -T w o s

C o m p le m e n tA r it h m e t ic

Overflow and Underflow

In performing arithmetic using two’s-complement arithmetic, we must be aware of the possibility of o v e r f lo w in which the result exceeds the maximum value that can be represented by the word length in use.

AAA =

AA =1

00 =A

BAAB =( ) ( ) ABCCABBCA ==

0=AA

AA =

( ) ( ) CBACBACBA ++=++=++

( ) ACABCBA +=+

AA =+ 0

11 =+A

1=+ AA

AAA =+

Boolean algebra expressions can be implemented by interconnection of AND gates, OR gates, and inverters.

’ D e M o r g a n s L a w s

CBAABC ++= ( ) FEDFED =++

If the variables in a logic expression are replaced by their inverses, the AND operation is replaced by OR, the OR operation is replaced by AND, and the entire expression is inverted, the resulting logic expression yields the same values as before the changes.

1 2C h a p t e r- F ie ld E f f e c t

T r a n s is t o r s

1. Understand MOSFET operation and small signal model (compare to BJTs).

3. See how FETs are used to build gates in CMOS Integrated Circuits (ICs) for computers.

N M O S A N D P M O ST R A N S IS T O R S

M O S F E T S u m m a r y

- -T h e F ix e d P lu s S e lf B ia s C ir c u it

- T h e S m a ll S ig n a l E q u iv a le n t C ir c u it

In small-signal midband analysis of FET amplifiers, the coupling capacitors, bypass capacitors, and dc voltage sources are replaced by short circuits. The FET is replaced with its small-signal equivalent circuit. Then, we write circuit equations and derive useful expressions for gains, input impedance, and output impedance (like earlier BJTs).

C M O S In v e r t e r

C M O S N A N D G a t e

C M O S N O R G a t e

, , N A N D N O R a n d X O R G a t e s

- - S u m o f P r o d u c t sIm p le m e n t a t io n

Product terms that include all of the input variables (or their inverses) are called m in t e r m s .

In a sum-of-products expression, we form a product of all the input variables (or their inverses) for each row of the truth table for which the result is logic 1. The output is the sum of these products.

- - P r o d u c t o f S u m sIm p le m e n t a t io n

Sum terms that include all of the input variables (or their inverses) are called m a x t e r m s .

In a product-of-sums expression, we form a sum of all the input variables (or their inverses) for each row of the truth table for which the result is logic 0. The output is the product of these sums.

Many useful combinatorial circuits known as d e c o d e r s , e n c o d e r s , or t r a n s la t o r s are available as integrated circuits.

K a r n a u g h M a p s

D IG IT A L S IG N A LP R O C E S S IN G

C o n v e r s io n o f S ig n a ls f r o m

A n a lo g t o D ig it a lF o r m

If a signal contains no components with frequencies higher than fH, the signal can be exactly reconstructed from its samples, providedthat the sampling rate fs is selected to be more than twice fH.

D ig it a l L o w p a s sF ilt e r

( ) ( ) ( ) ( )nxanayny −+−= 11

T

Ta

ττ+

=1

8C h a p t e rM ic r o c o m p u t e r s

1. Identify and describe the functional blocks of a microcomputer.

2. Select the type of memory needed for a given application.

An embedded computer is part of a product, such as an automobile, printer, or bread machine, that is not called a computer.

A microcomputer or microcontroller is a completecomputer containing the CPU, memory, and I/O on a single silicon chip.

This computer, in which the instructions and data arestored in the same memory, has von Neumannarchitecture (also known as Princeton architecture).

M E M O R Y T YP E S

(1) Read-and-write memory (RAM)

(2) Read-only memory (ROM)

(3) Mass storage - Disk, Flash(non volatile)

S e le c t io n o fM e m o r y

1 . The trade-off between speed and cost

2 . Whether the information is to be stored permanently or must be changed frequently

3 . Whether data are to be accessed in random order or in sequence

-A S S E M B L Y L A N G U A G E

P R O G R A M M IN G

In general, assembly language statements take the form:

LABEL INSTRUCTION/DIRECTIVE OPERAND COMMENT

D ir e c t iv e s are used to give commands to the assembler.

1. Compilers translate a higher level language, such as C and convert it into assembly (machine language) for a particular computer. Typically one C statement will generate several (5-10) assembly language statements

2. Most work is currently done using compilers and C. It’s faster and more cost effective to develop new applications.

3. Some tools like Labview can automatically generate C code.