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Digital Circuits Analog and Digital Signals Noise margins in Logic Circuits "1" V OH V IH V(y) V OH Undefined Region "0" V IL V OL Slope = -1 VM Slope = -1 VOL V V IL IH V(x) Noise margins in Logic Circuits VDD "1" V OH Noise margin high NMH V IH Undefined Region V OL "0" NML V IL VGND Gate Output Gate Input Noise margin low Digital to Binary Conversion Conversion of the integer part Digital to Binary Conversion Conversion of the fractional part Binary Addition A B C One bit binary adder A0 B0 C i,0 A1 S0 (= C i,1 ) Carry B1 Co,0 FA Sum A2 B2 C o,1 A3 B3 C o,2 Co,3 FA FA FA S1 S2 S3 Binary Coded Decimal and Hexadecimal Representation To get BCD replace each digit by a group of 4 bits 3786.1=0011 0111 1000 0110. 0001BCD 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 To get BCD replace each digit by a group of 4 bits 3786.1=0011 0111 1000 0110. 0001BCD Binary to hexadecimal conversion (0,1,..9,A,..,F) 1110 1010 1001 0101=EA9516 Exercise: Represent 25 by its BCD and binary codes 25 = 0010 0101BCD 25 = 0001 1001 25/2 = 12 12/2 = 6 6/2 = 3 3/2 = 1 1/2 = 0 rem 1 rem 0 rem 0 rem 1 rem 1 Binary and Grey Codes 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= 2) Find two’s complement of B -B= 3) Add A+(-B) using binary notation , B= 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=001011 2) Find two’s complement of B -B=110101 3) Add A+(-B) using binary notation 011001 +110101 001110 = 14
