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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

Karnaugh map or K-map discussion

It is a way of minimizing the Boolean functions using diagrams which are made up of squares. By minimization we imply a function with minimum number of terms and each term with lowest number of literals.

Following k-map for 2-5 variables are discussed in this section:

1) Two variables K-map

2) Three variables K-map

3) Four variables K-map

4) Five variables K-map

5) Prime Implicant and Gate level minimization examples

2 -Variable Karnaugh map (K-map) discussion below:

First write the Truth Table for 2 variables x and y. Once we know all the values in table its easier to plot the k-map.

2 variable K– map plot below : - Each element (0-3) from above table is plotted in k-map below. Var x is horizontal row and y is vertical column.  There intersection denotes output function element. 2 var KMAP below.

K-map location number
x
y
Output function
0
0
0
x’y’
1
0
1
x’y
2
1
0
xy’
3
1
1
xy

0

1

0

1

x

y

x’y’
x’y
xy’
xy
Misc. Verilog RTL examples:-
Binary to Gray Code conversion, File read write operations.
 Clock domain crossing., Half-adder, Full-adder, Tri-state buffer, Verilog testbench to validate half-adder, full-adder and tri-state buffer.
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 Clock Domain Crossing Discussion with rtl & testbench example.
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Prdt of Maxterms.
3 var K-map.
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 Difference between air, radio and core network..  
 Seamless mobility in 4G.
 LTE cells, network. UMTS LTE cell search, cell identities and synchronization signals (primary and secondary).  
 2X2 MIMO, DL MIMO frame format 2x2, UL MIMO frame format 2x2.
 4G LTE differences in FDD and TDD modes.
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2 variable solved k-map example link.