Digital Circuits

Analog and Digital Signals

Noise margins in Logic Circuits

"1"

"0"

VOH

VIH

VIL

VOL

UndefinedRegion

V(x)

V(y)

VOH

VOL

VIH

VIL

Slope = -1

Slope = -1

VM

Noise margins in Logic Circuits

Noise margin high

Noise margin low

VIH

VIL

UndefinedRegion

"1"

"0"

VOH

VOL

NMH

NML

Gate Output Gate Input

VDD

VGND

Digital to Binary Conversion

Conversion of the integer part

Digital to Binary Conversion

Conversion of the fractional part

Binary Addition

One bit binary adder

ABC

Sum Carry

FA FA FA FA

A0 B0

S0

A1 B1

S1

A2 B2

S2

A3 B3

S3

Ci,0 Co,0

(Ci,1)

Co,1 Co,2 Co,3

Binary Coded Decimal and Hexadecimal Representation

3786.1=0011 0111 1000 0110. 0001BCD

To get BCD replace each digit by a group of 4 bits

Binary to hexadecimal conversion (0,1,..9,A,..,F)

1110 1010 1001 0101=EA9516

Exercise: Represent 25 by its BCD and binary codes

Binary Coded Decimal and Hexadecimal Representation

3786.1=0011 0111 1000 0110. 0001BCD

To get BCD replace each digit by a group of 4 bits

Binary to hexadecimal conversion (0,1,..9,A,..,F)

1110 1010 1001 0101=EA9516

Exercise: Represent 25 by its BCD and binary codes

25/2 = 12 rem 112/2 = 6 rem 06/2 = 3 rem 03/2 = 1 rem 11/2 = 0 rem 1

25 = 0010 0101BCD

25 = 0001 1001

Binary and Grey Codes

Binary and Grey Codes

Two’s Complement and Binary Addition

One’s complement id obtained by inverting all the bitsTwo’s complement is obtained as one’s complement + 1

invert

Positive and Negative Binary Numbers

Signed two’s complement of a number is used a the negative number value. This can be used in subtraction operation.

Positive and Negative Binary Numbers

This can be used in subtraction operation.

To subtract number B from A we add two’s complement of B to A

Example: Compute A-B=25-11 using binary adders

1) Find binary representations A= , B= 2) Find two’s complement of B -B= 3) Add A+(-B) using binary notation

Positive and Negative Binary Numbers

This can be used in subtraction operation.

To subtract number B from A we add two’s complement of B to A

Example: Compute A-B=25-11 using binary adders

1) Find binary representations A=011001, B=0010112) Find two’s complement of B -B=1101013) Add A+(-B) using binary notation

011001+110101 001110 = 14