﻿ Kmap 4var      Custom Search Chip Designing for ASIC/ FPGA Design engineers and Students
FULLCHIPDESIGN
Digital-logic Design...  Dream for many students… start learning front-end…
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

4 variable K-map, Example -3

Minimize following

F(x,y,w, z) =     (0,2,5,7,8,11,13,15)

Above is a common format of representing the K-map problems. The numbers 0,2,5,7,8, 11,13,15 are the location of cells in the 4-var k-map table. Discussed below is a 4 variable K– map with 1 and 0 values. assigned to cells.

Interview Questions. Main, FPGA, Digital Fundamentals The minimization equation is shown below.
With reference to the table above the cells under the dotted box’s can be combined to come up with following reduced  equation.
F = w’y’ + yw .. Final Answer.
Resources
Clock Domain Crossing Discussion with rtl & testbench example. Rate change (asynchronous) FIFO design and fifo depth calculation. Half-adder, Full-adder, 4-bit binary adder , adder-subtractor circuit, overflow with rtl & testbench. Binary Multiplier, Parity error TT
Digital design Interview questions. FPGA Interview. FPGA flow. raduate studies in US pipeline vs. Parallel processing. Solved Examples for 3 variable Kmaps
1. F(x,y,z) =     (0,1,6,7) - Minimization, on this page.
2. F(x,y,z) =     (0,1,4,5,6,7) - Minimization from here.
3. F(x,y,z) =     (3,4,6,7) - Minimization from here.
4. F(x,y,z) =     (0,1,2,3,4,5,6,7) - Minimization from here.
MINIMIZATION USING FOUR VARIABLE KARNAUGH MAP

00

01

11

10

0

1

xy

zw

00

01

11

10

0

1

1

0

0

1

1

0

1

0

0

1

1

0  The K-map for 4 variables is plotted above. You will notice the column and rows for 11 and 10 are inter-changed. This is done to allow only one variable to change across adjacent cells. This adjustment in columns allows in minimization of logic mapped into tables.

Any adjacent 1, 2, 4 or 8 cells can be grouped to find a minimized logic value.   