Can you please change this text?

[Meenaharani]

I want to change a paragraph using appropraite sentence so if u can help me out please check it and sent the same i would be thank ful to you. Please change the paragrah it should not be as it is however the meaning should be the same



Transforming Circuits to CNF



In a logic circuit, the values assigned to internal circuit lines are constrained by the gates

attached to those lines. The output of an AND gate will be 1 iff all of its inputs are 1; the

output of an OR gate will be 0 iff all of its inputs are 0, and so on. Given any logic circuit,

a CNF formula can be constructed which expresses the same constraints. This is done by

generating sub-formulas expressing the constraints of each gate in the circuit, and then taking

the conjunction of all such sub-formulas.

A CNF formula representing the constraints for a gate can be generated from its charac-

teristic function [35]. This is a function χ(·) which evaluates to 1 if the values assigned to the

inputs and output of the gate are consistent, and 0 otherwise. The characteristic function can

be converted to a minimal CNF formula by means of a Karnaugh map [26: p. 452] or any other

standard logic minimization technique. For example, the characteristic function for an AND gate

with inputs x1 and x2 and output y is shown in Figure 2.1.

This process can be repeated for any gate type, including multi-output gates. The construc-

tion will be polynomial in the number of inputs and outputs as long as “counting”-type gates

are assumed to have a fixed maximum number of inputs [9]. Table 2.1 gives the CNF formulas

for all gate types which are used in the algorithms presented in this thesis. Note that inverted

gate types like NAND and NOR can be made from their non-inverting counterparts by negating

the output literal wherever it appears in the formula. Compare, for example, the CNF formula

for the NAND gate to that for the AND gate.

The last three gates in the table are the multiplexer (mux), half-adder, and full-adder gates.

The mux is used heavily in Section 4.2 and Chapter 5. The adders are used in Section 4.3.

These are not always considered to be “elementary” gate types. They are usually built up

from several of the other gate types listed. However, it is often beneficial not to decompose

them into simpler gate types, since doing so will usually result in a larger CNF formula. For

example, the MUX gate can be decomposed into three NAND gates and a NOT gate, but doing so

would result in a CNF formula with eleven clauses instead of four. Taking the conjunction of

the sub-formulas for each gate in a circuit results in a CNF formula that represents the entire

circuit. Any variable assignment that satisfies this formula directly yields a valid assignment of

logic values to circuit lines

[Luschen]

I am not a teacher, but I am an electrical engineer. I couldn't find any grammatical mistakes in the text. Is has been a long time since I have used logic gates though, so I can't attest to your text's factual accuracy.

[E2e4]

Seems to me that the paragraph consists of a few sentences in which digital terminology is used but the paragraph explains almost nothing.

Anyway Karnaugh mapping is a graphical method for minimasing the transfer function of a complex digital circuit consisting of a lot of elementary circuits.