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

以下是一个简单的实现，可以在Qt中运行，实现不同进制之间的相互转换，并且能够保存历史记录，支持多次转换和重新输入：

#include <QApplication>
#include <QMainWindow>
#include <QLabel>
#include <QLineEdit>
#include <QPushButton>
#include <QHBoxLayout>
#include <QVBoxLayout>
#include <QMessageBox>
#include <QFileDialog>
#include <QFile>
#include <QTextStream>
#include <QDateTime>
#include <QDebug>

class Converter : public QObject {
    Q_OBJECT

public:
    Converter() {
        // 初始化界面元素
        window = new QMainWindow();
        window->setWindowTitle("进制转换器");

        inputLineEdit = new QLineEdit();
        outputLineEdit = new QLineEdit();
        outputLineEdit->setReadOnly(true);

        binaryButton = new QPushButton("二进制");
        octalButton = new QPushButton("八进制");
        decimalButton = new QPushButton("十进制");
        hexadecimalButton = new QPushButton("十六进制");

        convertButton = new QPushButton("转换");
        clearButton = new QPushButton("清空");
        saveButton = new QPushButton("保存记录");
        loadButton = new QPushButton("加载记录");

        QHBoxLayout* inputLayout = new QHBoxLayout();
        inputLayout->addWidget(new QLabel("输入："));
        inputLayout->addWidget(inputLineEdit);

        QHBoxLayout* outputLayout = new QHBoxLayout();
        outputLayout->addWidget(new QLabel("输出："));
        outputLayout->addWidget(outputLineEdit);

        QVBoxLayout* buttonLayout = new QVBoxLayout();
        buttonLayout->addWidget(binaryButton);
        buttonLayout->addWidget(octalButton);
        buttonLayout->addWidget(decimalButton);
        buttonLayout->addWidget(hexadecimalButton);
        buttonLayout->addStretch();
        buttonLayout->addWidget(convertButton);
        buttonLayout->addWidget(clearButton);
        buttonLayout->addWidget(saveButton);
        buttonLayout->addWidget(loadButton);

        QVBoxLayout* mainLayout = new QVBoxLayout();
        mainLayout->addLayout(inputLayout);
        mainLayout->addLayout(outputLayout);
        mainLayout->addLayout(buttonLayout);

        QWidget* centralWidget = new QWidget();
        centralWidget->setLayout(mainLayout);

        window->setCentralWidget(centralWidget);

        // 连接信号与槽
        connect(binaryButton, &QPushButton::clicked, this, &Converter::binaryButtonClicked);
        connect(octalButton, &QPushButton::clicked, this, &Converter::octalButtonClicked);
        connect(decimalButton, &QPushButton::clicked, this, &Converter::decimalButtonClicked);
        connect(hexadecimalButton, &QPushButton::clicked, this, &Converter::hexadecimalButtonClicked);
        connect(convertButton, &QPushButton::clicked, this, &Converter::convertButtonClicked);
        connect(clearButton, &QPushButton::clicked, this, &Converter::clearButtonClicked);
        connect(saveButton, &QPushButton::clicked, this, &Converter::saveButtonClicked);
        connect(loadButton, &QPushButton::clicked, this, &Converter::loadButtonClicked);
    }

    void show() {
        window->show();
    }

private:
    QMainWindow* window;
    QLineEdit* inputLineEdit;
    QLineEdit* outputLineEdit;
    QPushButton* binaryButton;
    QPushButton* octalButton;
    QPushButton* decimalButton;
    QPushButton* hexadecimalButton;
    QPushButton* convertButton;
    QPushButton* clearButton;
    QPushButton* saveButton;
    QPushButton* loadButton;
    QStringList history;

    enum class Base {
        Binary,
        Octal,
        Decimal,
        Hexadecimal
    };

    void convert(Base from, Base to) {
        QString input = inputLineEdit->text();

        // 判断输入是否合法
        bool ok;
        int inputInt;
        switch (from) {
        case Base::Binary:
            inputInt = input.toInt(&ok, 2);
            break;
        case Base::Octal:
            inputInt = input.toInt(&ok, 8);
            break;
        case Base::Decimal:
            inputInt = input.toInt(&ok, 10);
            break;
        case Base::Hexadecimal:
            inputInt = input.toInt(&ok, 16);
            break;
        }
        if (!ok) {
            QMessageBox::warning(window, "错误", "输入不合法！");
            return;
        }

        // 进行转换
        QString output;
        switch (to) {
        case Base::Binary:
            output = QString::number(inputInt, 2);
            break;
        case Base::Octal:
            output = QString::number(inputInt, 8);
            break;
        case Base::Decimal:
            output = QString::number(inputInt, 10);
            break;
        case Base::Hexadecimal:
            output = QString::number(inputInt, 16).toUpper();
            break;
        }

        // 更新输出框
        outputLineEdit->setText(output);
        outputLineEdit->selectAll();

        // 添加历史记录
        QString item = QString("%1 %2 %3").arg(input).arg(getBaseName(from)).arg(getBaseName(to));
        history.append(item);
    }

    QString getBaseName(Base base) {
        switch (base) {
        case Base::Binary:
            return "二进制";
        case Base::Octal:
            return "八进制";
        case Base::Decimal:
            return "十进制";
        case Base::Hexadecimal:
            return "十六进制";
        }
        return "";
    }

private slots:
    void binaryButtonClicked() {
        convert(Base::Decimal, Base::Binary);
    }

    void octalButtonClicked() {
        convert(Base::Decimal, Base::Octal);
    }

    void decimalButtonClicked() {
        convert(Base::Hexadecimal, Base::Decimal);
    }

    void hexadecimalButtonClicked() {
        convert(Base::Decimal, Base::Hexadecimal);
    }

    void convertButtonClicked() {
        bool ok;
        int inputInt = inputLineEdit->text().toInt(&ok);
        if (!ok) {
            QMessageBox::warning(window, "错误", "输入不合法！");
            return;
        }

        // 判断原进制
        Base from;
        if (inputLineEdit->text().startsWith("0b")) {
            from = Base::Binary;
        } else if (inputLineEdit->text().startsWith("0")) {
            from = Base::Octal;
        } else if (inputLineEdit->text().startsWith("0x")) {
            from = Base::Hexadecimal;
        } else {
            from = Base::Decimal;
        }

        // 判断目标进制
        Base to;
        if (binaryButton->isChecked()) {
            to = Base::Binary;
        } else if (octalButton->isChecked()) {
            to = Base::Octal;
        } else if (decimalButton->isChecked()) {
            to = Base::Decimal;
        } else if (hexadecimalButton->isChecked()) {
            to = Base::Hexadecimal;
        } else {
            QMessageBox::warning(window, "错误", "请选择目标进制！");
            return;
        }

        convert(from, to);
    }

    void clearButtonClicked() {
        inputLineEdit->clear();
        outputLineEdit->clear();
    }

    void saveButtonClicked() {
        QString fileName = QFileDialog::getSaveFileName(window, "保存记录", "", "Text files (*.txt)");
        if (fileName.isEmpty()) {
            return;
        }

        QFile file(fileName);
        if (!file.open(QIODevice::WriteOnly | QIODevice::Text)) {
            QMessageBox::warning(window, "错误", QString("无法保存文件 %1！").arg(fileName));
            return;
        }

        QTextStream out(&file);
        for (const QString& item : history) {
            out << item << "\n";
        }

        QMessageBox::information(window, "保存记录", QString("记录已保存到文件 %1！").arg(fileName));
    }

    void loadButtonClicked() {
        QString fileName = QFileDialog::getOpenFileName(window, "加载记录", "", "Text files (*.txt)");
        if (fileName.isEmpty()) {
            return;
        }

        QFile file(fileName);
        if (!file.open(QIODevice::ReadOnly | QIODevice::Text)) {
            QMessageBox::warning(window, "错误", QString("无法加载文件 %1！").arg(fileName));
            return;
        }

        QStringList newHistory;
        QTextStream in(&file);
        while (!in.atEnd()) {
            QString line = in.readLine();
            newHistory.append(line);
        }

        history = newHistory;
        QMessageBox::information(window, "加载记录", QString("已从文件 %1 加载 %2 条记录！").arg(fileName).arg(history.size()));
    }
};

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

    Converter converter;
    converter.show();

    return app.exec();
}

#include "main.moc"

编译运行后，会弹出一个界面，可以输入数字进行转换，也可以选择不同的进制进行转换，还可以保存和加载历史记录：

注意，代码中使用了Qt的信号与槽机制，需要添加 `#include "main.moc"` 才能正确编译。