The construction of the K-Map with about six ones and three don’t cares
The K map is a simplified way of solving the circuit equations. as an alternative of using Boolean algebra generalization techniques, one can shift logic digits from a Boolean equation or a truth table into a K map. The assortments of 0’s and 1’s inside the map enables one to picture out the logic interrelations between the variables and enables an easily understood Boolean statement. These maps are usually used to evaluate logic problems with particular variables. Variables in Karnaugh maps are used to introduce the actual methods one might need in order to learn. The map for a 4-input OR gate for instance can be represented as:
BA
00 01 11 10
00 0 0 1 0
01 0 1 1 1
11 1 1 0 0
10 0 1 0 0
DC
Use the ones and any useful don’t cares (to simplify the equation) to create F as a SOP equation of essential prime implicants
In order to evaluate and simplify the particular referred equation from the above K map:
To obtain the simplest Boolean statement, you have to encircle the maximum number of the terms. Here one can make two groups of each four, one of one binding the top to bottom. Then the variables that remain constant in each case and do away with the other remaining two hence the simplified equation obtained is:
X=B.D+B.C
2. Use the zeros and useful don’t cares (to simplify the equation) to create an F’ equation of essential prime implicants
The first of terms in the Boolean total sum-of-products expression is given by AC
We realize that A and B retain the same status, but C and vary B is 0 and has to be negative before inclusion. Hence the second term is AB
Similarly the subsequent grouping shows the BCD
Therefore the results AC+AB+BCD But reciprocating with zeros instead.
This yields the inverse: thus De Morgan’s law
F=AB+AC+BCD
3. Use DeMorgan’s Law to convert the F’ equation into F as a POS equation
Through the use of De Morgan’s laws, the product of sums can be determined:
F=AB+AC+BCD
F=(A+B)(A+C)(B+C+D)
Show your understanding of that simple ALU by giving the following for a set of inputs based on the 5 bit binary representation.
1) The output and carry out outputs
The output of the ALU is a given specified set of programmed conditions or codes towards or from a status register and this relies on the direction of movement. The codes are then indicated as the carry in or the alternative carry out. They can also imply the overflow or divide-by-zero depending on the magnitude.
2) The type of calculation (AND, OR, NOT, or plus)Where the 5-bit inputs represent A, B, Carry-in, I1, and I0 respectively. For example: “1. Elizabeth Ballard” has a binary value of 00001 with A= 0, B=0, Carry-in =0, I1 = 0, and I0 = 1
The given three F/alu bits ( also known as function bits for the ALU) present the choice of the arithmetic function, for the one specific bit the of the three F/alu bits give the selection of the arithmetic function, the one bit of F/cy (function bit for carry selection) reins the multiplexer and thus the feed-in required signal, they influence the task of the individual arithmetic unit.
Reference
Tamma V (2005). Ontologies for agents: theory and experiences Whitestein series in software agent technologies London: Birkhäuser
