#ifndef MAINWINDOW_H
#define MAINWINDOW_H

#include "ui_mainwindow.h"
#include <QProcess>

class MainWindow : public QMainWindow, private Ui::MainWindow
{
    Q_OBJECT
    
public:
    explicit MainWindow(QWidget *parent = 0);
    QProcess *myprocess;
private slots:
    void on_pushButton_clicked();
    void outExec();
    void finishExec ( int exitCode, QProcess::ExitStatus exitStatus );
};

#endif // MAINWINDOW_H

#include "mainwindow.h"
#include <QDebug>
#include <QDir>

MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent)
{
    setupUi(this);
}

void MainWindow::on_pushButton_clicked()
{
    QString programm =  lineEdit->text();
    myprocess = new QProcess(this);
    myprocess->setObjectName(programm);
    //myprocess->start(QString("exec\\" + programm).toAscii());
    myprocess->start(QString("cmd /C " + QDir::currentPath() + "/exec/" + programm).toAscii());
    qDebug() << "RUN " << QString("cmd /C " + QDir::currentPath() + "/exec/" + programm).toAscii();
    connect(myprocess, SIGNAL(readyReadStandardOutput ()), this, SLOT(outExec()));
    connect(myprocess, SIGNAL(finished (int,QProcess::ExitStatus)), this, SLOT(finishExec(int,QProcess::ExitStatus)));
}

void MainWindow::outExec()
{
    QString out = myprocess->readAllStandardOutput();
    qDebug() << "__" << out;
    plainTextEdit->appendPlainText(QString(out));
}

void MainWindow::finishExec ( int exitCode, QProcess::ExitStatus exitStatus )
{
    QString out = myprocess->readAllStandardOutput();
    qDebug() << out;
    plainTextEdit->appendPlainText(QString(out));
}

connect(myprocess, SIGNAL(readyReadStandardError ()), this, SLOT(outExec()));
И в обоих функциях 
QTextCodec *codec = QTextCodec::codecForName("CP866");  //Windows-1251 CP1251 KOI8-R
    out += codec->toUnicode(myprocess->readAllStandardError());

myprocess->setStandardOutputFile(programm + ".log",QIODevice::WriteOnly);
            myprocess->setObjectName(programm);

QString name = currentProcess->objectName();
        QFile file;
        file.setFileName(name + ".log");
        if (!file.open(QIODevice::ReadOnly | QIODevice::Text))
        {
            return;
        }
        else
        {
            QString logFile;
            QTextStream in(&file);
            while (!in.atEnd())
            {
                logFile += in.readLine();
            }
            if (logFile!="")
                textEdit->setText(logFile);
            else
                return;
        }