digital circuits
DESCRIPTION
Digital Circuits. Analog and Digital Signals. V M. Noise margins in Logic Circuits. V DD. "1". V. OH. Noise margin high. NM. H. V. IH. Undefined. Region. V. NM. Noise margin low. L. IL. V. OL. "0". V GND. Gate Input. Gate Output. Noise margins in Logic Circuits. - PowerPoint PPT PresentationTRANSCRIPT
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