Digital Circuits. Analog and Digital Signals Noise margins in Logic Circuits VMVM.

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Presentation transcript:

Digital Circuits

Analog and Digital Signals

Noise margins in Logic Circuits VMVM

Noise margin high Noise margin low V IH V IL Undefined Region "1" "0" V OH V OL NM H L Gate Output Gate Input V DD V GND

Digital to Binary Conversion Conversion of the integer part

Digital to Binary Conversion Conversion of the fractional part

Binary Addition One bit binary adder ABCABC Sum Carry FA A 0 B 0 S 0 A 1 B 1 S 1 A 2 B 2 S 2 A 3 B 3 S 3 C i,0 C o (  C i,1 ) C o C o,2 C o,3

Binary Coded Decimal and Hexadecimal Representation = BCD To get BCD replace each digit by a group of 4 bits Binary to hexadecimal conversion (0,1,..9,A,..,F) =EA95 16 Exercise: Represent 25 by its BCD and binary codes

Binary Coded Decimal and Hexadecimal Representation = BCD To get BCD replace each digit by a group of 4 bits Binary to hexadecimal conversion (0,1,..9,A,..,F) =EA95 16 Exercise: Represent 25 by its BCD and binary codes 25/2 = 12 rem 1 12/2 = 6 rem 0 6/2 = 3 rem 0 3/2 = 1 rem 1 1/2 = 0 rem 1 25 = BCD 25 =

Binary and Grey Codes

Two’s Complement and Binary Addition One’s complement id obtained by inverting all the bits Two’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= )Find two’s complement of B -B= )Add A+(-B) using binary notation = 14

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