Fault of Electric Cable
Energy Bands in Crystals
Gallium Arsenide Semiconductor
Atomic Energy Levels
Electric Pressure Cooker
Boolean Algebra Theorems and Laws of Boolean Algebra
De Morgan Theorem and Demorgans Laws
Truth Tables for Digital Logic
Simplifying Boolean Expression using K Map
Excess 3 Code Addition and Subtraction
K Map or Karnaugh Map
Switching Algebra or Boolean Algebra
Binary Adder Half and Full Adder
Seven Segment Display
Binary to Gray Code Converter and Grey to Binary Code Converter
Binary to BCD Code Converter
Analog to Digital Converter
Digital Encoder or Binary Encoder
Basic Digital Counter
BCD to Seven Segment Decoder
OR Operation | Logical OR Operation
AND Operation | Logical AND Operation
Logical OR Gate
Logical AND Gate
Universal Gate | NAND and NOR Gate as Universal Gate
Diode and Transistor NAND Gate or DTL NAND Gate and NAND Gate ICs
X OR Gate and X NOR Gate
Transistor Transistor Logic or TTL
Fan out of Logic Gates
NMOS Logic and PMOS Logic
Logic Families Significance and Types of Logic Families
Binary Number System | Binary to Decimal and Decimal to Binary Conversion
Binary to Decimal and Decimal to Binary Conversion
BCD or Binary Coded Decimal | BCD Conversion Addition Subtraction
Binary to Octal and Octal to Binary Conversion
Octal to Decimal and Decimal to Octal Conversion
Binary to Hexadecimal and Hex to Binary Conversion
Hexadecimal to Decimal and Decimal to Hexadecimal Conversion
Gray Code | Binary to Gray Code and that to Binary Conversion
Octal Number System
Digital Logic Gates
2s Complement Arithmetic
Error Detection and Correction Codes
9s complement and 10s complement | Subtraction
Some Common Applications of Logic Gates
Alphanumeric codes | ASCII code | EBCDIC code | UNICODE
Latches and Flip Flops
S R Flip Flop S R Latch
Active Low S R Latch and Flip Flop
Gated S R Latches or Clocked S R Flip Flops
D Flip Flop or D Latch
J K Flip Flop
Master Slave Flip Flop
Read Only Memory | ROM
Programmable Logic Devices
Programmable Array Logic
Application of Flip Flops
Buffer Register and Controlled Buffer Register
Data Transfer in Shift Registers
Serial In Serial Out (SISO) Shift Register
Serial in Parallel Out (SIPO) Shift Register
Parallel in Serial Out (PISO) Shift Register
Parallel in Parallel Out (PIPO) Shift Register
Universal Shift Registers
Bidirectional Shift Register
Dynamic Shift Register
Conversion of Flip Flops
Simplifying Boolean Expression using K Map
Minterm Solution of K MapThe following are the steps to obtain simplified minterm solution using K-map. Step 1: Initiate Express the given expression in its canonical form Step 2: Populate the K-map Enter the value of 'one' for each product-term into the K-map cell, while filling others with zeros. Step 3: Form Groups
- Consider the consecutive 'ones' in the K-map cells and group them (green boxes).
- Each group should contain the largest number of 'ones' and no blank cell.
- The number of 'ones' in a group must be a power of 2 i.e. a group can contain
- Grouping has to be carried-on in decreasing order meaning, one has to try to group for 8 (octet) first, then for 4 (quad), followed by 2 and lastly for 1 (isolated 'ones').
- Grouping is to done either horizontally or vertically or interms of squares or rectangles. Diagonal grouping of 'ones' is not permitted.
- The same element(s) may repeat in multiple groups only if this increases the size of the group.
- The elements around the edges of the table are considered to be adjacent and can be grouped together.
- Don’t care conditions are to be considered only if they aid in increasing the group-size (else neglected).
Express each group interms of input variables by looking at the common variables seen in cell-labelling. For example in the figure shown below there are two groups with two and one number of 'ones' in them (Group 1 and Group 2, respectively). All the 'ones' in the Group 1 of the K-map are present in the row for which A = 0. Thus they contain the variable A̅. Further these two 'ones' are present in adjacent columns which have only B term in common as indicated by the pink arrow in the figure.
Hence the next term is B. This yields the product term corresponding to this group as A̅B. Similarly the 'one' in the Group 2 of the K-map is present in the row for which A = 1. Further the variables corresponding to its column are B̅C̅. Thus one gets the overall product-term for this group as AB̅C̅. Step 5: Obtain Boolean Expression for the Output The product-terms obtained for individual groups are to be combined to form sum-of-product (SOP) form which yields the overall simplified Boolean expression. This means that for the K-map shown in Step 4, the overall simplified output expression is A few more examples elaborating K-map simplification process are shown below.
Maxterm Solution of K MapThe method to be followed in order to obtain simplified maxterm solution using K-map is similar to that for minterm solution except minor changes listed below.
- K-map cells are to be populated by 'zeros' for each sum-term of the expression instead of 'ones'.
- Grouping is to be carried-on for 'zeros' and not for 'ones'.
- Boolean expressions for each group are to be expressed as sum-terms and not as product-terms.
- Sum-terms of all individual groups are to be combined to obtain the overall simplified Boolean expression in product-of-sums (POS) form.