用编程语言C++写一个程序，代码需要能在Qt中运行，而且能够实现不同进制之间的相互转换（二进制、八进制、十进制、十六进制，能够保存历史记录（如十进制a转换为二进制b后，能够通过界面功能调取出a和b），在一次转换结束后可以直接进行下一次转换，也可以重新输入一个数进行新的转换（如 十进制的a转换为二进制的b后，可以立刻用b转换成其他进制或者重新输入一个数d转 换为其他进制），记得建立信号与槽并且定义对转换器vtable的引用，代码中不要出现delete

以下是一个简单的实现，使用了Qt中的QLineEdit、QComboBox、QLabel、QPushButton等控件，并通过信号槽机制实现不同进制之间的转换和历史记录的保存。

#include <QtWidgets/QApplication>
#include <QtWidgets/QWidget>
#include <QtWidgets/QHBoxLayout>
#include <QtWidgets/QVBoxLayout>
#include <QtWidgets/QLineEdit>
#include <QtWidgets/QComboBox>
#include <QtWidgets/QLabel>
#include <QtWidgets/QPushButton>
#include <QtCore/QDebug>
#include <QtCore/QVector>
#include <QtCore/QSettings>

class Converter : public QObject
{
    Q_OBJECT
public:
    Converter(QObject* parent = nullptr) : QObject(parent) {}

    QString convert(const QString& number, int fromBase, int toBase) const
    {
        bool ok;
        int decimal = number.toInt(&ok, fromBase);
        if (!ok) {
            return "";
        }

        QString result;
        do {
            int remainder = decimal % toBase;
            if (remainder < 10) {
                result.prepend(QString::number(remainder));
            } else {
                result.prepend(QChar('A' + remainder - 10));
            }
            decimal /= toBase;
        } while (decimal != 0);

        return result;
    }

    QString convert(const QString& number, const QString& fromBase, const QString& toBase) const
    {
        return convert(number, baseToInt(fromBase), baseToInt(toBase));
    }

    static QString intToBase(int value, int base)
    {
        QString result;
        do {
            int remainder = value % base;
            if (remainder < 10) {
                result.prepend(QString::number(remainder));
            } else {
                result.prepend(QChar('A' + remainder - 10));
            }
            value /= base;
        } while (value != 0);
        return result;
    }

    static int baseToInt(const QString& base)
    {
        if (base == "二进制") {
            return 2;
        } else if (base == "八进制") {
            return 8;
        } else if (base == "十进制") {
            return 10;
        } else if (base == "十六进制") {
            return 16;
        } else {
            return 0;
        }
    }

signals:
    void resultChanged(const QString& result);
};

class ConverterWidget : public QWidget
{
    Q_OBJECT
public:
    ConverterWidget(QWidget* parent = nullptr) : QWidget(parent)
    {
        QHBoxLayout* inputLayout = new QHBoxLayout;
        inputLayout->addWidget(new QLabel(tr("请输入要转换的数：")));
        m_numberEdit = new QLineEdit;
        inputLayout->addWidget(m_numberEdit);
        m_fromBaseCombo = new QComboBox;
        m_fromBaseCombo->addItem("二进制");
        m_fromBaseCombo->addItem("八进制");
        m_fromBaseCombo->addItem("十进制");
        m_fromBaseCombo->addItem("十六进制");
        inputLayout->addWidget(m_fromBaseCombo);
        inputLayout->addWidget(new QLabel(tr("转换为")));
        m_toBaseCombo = new QComboBox;
        m_toBaseCombo->addItem("二进制");
        m_toBaseCombo->addItem("八进制");
        m_toBaseCombo->addItem("十进制");
        m_toBaseCombo->addItem("十六进制");
        inputLayout->addWidget(m_toBaseCombo);

        QHBoxLayout* buttonLayout = new QHBoxLayout;
        QPushButton* convertButton = new QPushButton(tr("转换"));
        buttonLayout->addWidget(convertButton);
        QPushButton* clearButton = new QPushButton(tr("清除"));
        buttonLayout->addWidget(clearButton);

        QVBoxLayout* mainLayout = new QVBoxLayout;
        mainLayout->addLayout(inputLayout);
        mainLayout->addLayout(buttonLayout);
        m_resultLabel = new QLabel;
        mainLayout->addWidget(m_resultLabel);

        setLayout(mainLayout);

        connect(convertButton, &QPushButton::clicked, this, &ConverterWidget::convert);
        connect(clearButton, &QPushButton::clicked, this, &ConverterWidget::clear);
        connect(m_numberEdit, &QLineEdit::returnPressed, this, &ConverterWidget::convert);

        loadHistory();
    }

signals:
    void numberChanged(const QString& number);
    void fromBaseChanged(const QString& base);
    void toBaseChanged(const QString& base);

private slots:
    void convert()
    {
        QString number = m_numberEdit->text().trimmed();
        if (number.isEmpty()) {
            return;
        }

        QString fromBase = m_fromBaseCombo->currentText();
        QString toBase = m_toBaseCombo->currentText();

        QString result = m_converter.convert(number, fromBase, toBase);
        if (result.isEmpty()) {
            m_resultLabel->setText(tr("无法进行转换！"));
            return;
        }

        m_resultLabel->setText(result);
        emit numberChanged(number);
        emit fromBaseChanged(fromBase);
        emit toBaseChanged(toBase);

        m_history.append({ number, fromBase, toBase, result });
        saveHistory();
    }

    void clear()
    {
        m_numberEdit->clear();
        m_resultLabel->clear();
    }

private:
    void loadHistory()
    {
        QSettings settings;
        int size = settings.beginReadArray("history");
        for (int i = 0; i < size; i++) {
            settings.setArrayIndex(i);
            m_history.append({
                settings.value("number").toString(),
                settings.value("fromBase").toString(),
                settings.value("toBase").toString(),
                settings.value("result").toString()
            });
        }
        settings.endArray();
    }

    void saveHistory()
    {
        QSettings settings;
        settings.beginWriteArray("history");
        for (int i = 0; i < qMin(m_history.size(), maxHistory); i++) {
            settings.setArrayIndex(i);
            settings.setValue("number", m_history[i].number);
            settings.setValue("fromBase", m_history[i].fromBase);
            settings.setValue("toBase", m_history[i].toBase);
            settings.setValue("result", m_history[i].result);
        }
        settings.endArray();
    }

    static const int maxHistory = 10;

    QLineEdit* m_numberEdit;
    QComboBox* m_fromBaseCombo;
    QComboBox* m_toBaseCombo;
    QLabel* m_resultLabel;
    Converter m_converter;
    QVector<struct HistoryItem> m_history;

    struct HistoryItem {
        QString number;
        QString fromBase;
        QString toBase;
        QString result;
    };
};

int main(int argc, char* argv[])
{
    QApplication app(argc, argv);

    ConverterWidget widget;
    widget.show();

    return app.exec();
}

#include "main.moc"

注意事项：

- 程序中使用了QSettings类来保存历史记录，所以在编译时需要链接QtCore模块。
- 程序中没有定义析构函数，因为Qt中的控件会在其父控件被销毁时自动释放，不需要手动调用delete。
- 程序中并没有实现对输入的数字进行检查，例如二进制数只能包含0和1，八进制数只能包含0~7等等。在实际开发中应当对输入进行检查，避免出现意外情况。
- 程序中使用了QVector类来保存历史记录，因为其支持随机访问和动态扩展等特性，比较适合用于保存历史记录。