1. Digital Circuits

2. Analog and Digital Signals

4. Noise margins in Logic Circuits VMVM

5. 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

6. Digital to Binary Conversion Conversion of the integer part

7. Digital to Binary Conversion Conversion of the fractional part

8. 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

9. Binary Coded Decimal and Hexadecimal Representation 3786.1=0011 0111 1000 0110. 0001 BCD 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=EA95 16 Exercise: Represent 25 by its BCD and binary codes

10. Binary Coded Decimal and Hexadecimal Representation 3786.1=0011 0111 1000 0110. 0001 BCD 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=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 = 0010 0101 BCD 25 = 0001 1001

11. Binary and Grey Codes

13. 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

14. 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.

15. 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

16. 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