A base converter supporting fractions, negative number and even negative base, and it has commands and graphical user interface.

converter.py

#!/usr/bin/env python3.8
# -*- coding: utf-8 -*-

__all__ = ['mod', 'to_decimal', 'to_base', 'convert', 'DEFAULT_TABLE']

from math import ceil, floor
from string import ascii_lowercase, ascii_uppercase, digits
from typing import Tuple, Union

DEFAULT_TABLE = digits + ascii_uppercase + ascii_lowercase


def mod(dividend: int, divisor: int) -> Tuple[int, int]:
    quotient, remainder = dividend // divisor, dividend % divisor
    if remainder < 0:
        quotient += 1
        remainder -= divisor
    return quotient, remainder


def to_decimal(number: str, base: Union[int, str], table: str = DEFAULT_TABLE) -> Union[int, float]:
    base = int(base)

    position = number.find('.')

    if number[0] == '-':
        negative = True
        number = number[1:]
    else:
        negative = False

    if position == -1:
        result, index = 0, 1
        for digit in number[::-1]:
            result += index * table.find(digit)
            index *= base
    else:
        integer, fraction = number.split('.')
        result, index = to_decimal(integer, base, table), 1.0
        for digit in fraction:
            index /= base
            result += index * table.find(digit)

    return -result if negative else result


def to_base(number: Union[int, float], base: Union[int, str], table: str = DEFAULT_TABLE) -> str:
    try:
        base = int(base)
    except ValueError:
        pass

    if number == 0:
        return table[0] if isinstance(number, int) else '{}.{}'.format(table[0], table[0])

    result_numbers = []
    if number < 0 < base:
        negative = True
        number = abs(number)
    else:
        negative = False

    if isinstance(number, int):
        while number != 0:
            number, remainder = mod(number, base)
            result_numbers.insert(0, table[remainder])
    else:
        integer = ceil(number) if base < 0 else floor(number)
        fraction = number - integer
        result_numbers.append(to_base(integer, base, table) + '.')
        times = 0
        while fraction != 0 and times < 100:
            fraction *= base
            integer = ceil(fraction) if base < 0 else floor(fraction)
            fraction -= integer
            result_numbers.append(table[integer])
            times += 1
        if times == 0:
            result_numbers.append(table[0])

    if negative:
        result_numbers.insert(0, '-')
    return ''.join(result_numbers)


def convert(number: str, original_base: Union[int, str] = 0, result_base: Union[int, str] = 10,
            table: str = DEFAULT_TABLE) -> str:
    original_base, result_base = int(original_base), int(result_base)
    if original_base == result_base:
        return number
    return to_base(to_decimal(number, original_base, table), result_base, table)

gui.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from PyQt5.QtWidgets import QMainWindow, QApplication
from PyQt5.QtCore import pyqtSignal
from MainWindow import Ui_MainWindow
import sys
from converter import convert, DEFAULT_TABLE


class MainWindow(QMainWindow, Ui_MainWindow):
    number_changed = pyqtSignal(str, name='numberChanged')
    result_changed = pyqtSignal(str, name='resultChanged')

    def __init__(self, number: str = None, original_base: int = 10, result_base: int = 10, table: str = None):
        super().__init__(None)
        self.setupUi(self)

        self.computing = False

        self.number_changed['QString'].connect(self.resultNumberLineEdit.setText)
        self.result_changed['QString'].connect(self.originalNumberLineEdit.setText)
        self.originalNumberLineEdit.textEdited.connect(lambda: self.compute(True))
        self.resultNumberLineEdit.textEdited.connect(lambda: self.compute(False))

        self.originalBaseLineEdit.setText(str(original_base))
        self.resultBaseLineEdit.setText(str(result_base))
        if table and table != DEFAULT_TABLE:
            self.usingTableCheckBox.setChecked(True)
            self.tableLabel.setEnabled(True)
            self.tableLineEdit.setEnabled(True)
            self.tableLineEdit.setText(table)
        if number:
            self.originalNumberLineEdit.setText(number)
            self.compute(True)

    def compute(self, from_number: bool):
        if from_number:
            number = self.originalNumberLineEdit.text()
            original_base = self.originalBaseLineEdit.text()
            result_base = self.resultBaseLineEdit.text()
        else:
            number = self.resultNumberLineEdit.text()
            original_base = self.resultBaseLineEdit.text()
            result_base = self.originalBaseLineEdit.text()
        table = self.tableLineEdit.text() if self.usingTableCheckBox.isChecked() else DEFAULT_TABLE

        try:
            result = convert(number, original_base, result_base, table)
        except (ValueError, IndexError):
            result = ''
        if from_number:
            self.number_changed[str].emit(result)
        else:
            self.result_changed[str].emit(result)


def start(number: str = None, original_base: int = 10, result_base: int = 10, table: str = None):
    application = QApplication([])
    main_window = MainWindow(number, original_base, result_base, table)
    main_window.show()
    sys.exit(application.exec())


if __name__ == '__main__':
    start()

main.py

#!/usr/bin/env python3.8
# -*- coding: utf-8 -*-

from typing import Optional

import click

from converter import DEFAULT_TABLE, convert
from gui import start as gui_start


@click.command()
@click.option('-g', '--gui', is_flag=True, help='Open Graphical User Interface.')
@click.option('-n', '--number', type=click.STRING, help='Set the number.')
@click.option('-o', '--original-base', type=click.INT, help='Set original base.')
@click.option('-r', '--result-base', type=click.INT, help='Set result base.')
@click.option('-t', '--table', type=click.STRING, help='Set the table.')
@click.argument('others', nargs=-1)
def process(gui: bool,
            number: Optional[str], original_base: Optional[int], result_base: Optional[int], table: Optional[str],
            others: tuple):
    for arg in others:
        if number is None:
            number = arg
        elif original_base is None:
            original_base = arg
        elif result_base is None:
            result_base = arg
        elif table is None:
            table = arg
    original_base = original_base or 10
    result_base = result_base or 10
    table = table or DEFAULT_TABLE

    if not gui:
        click.echo(convert(number, original_base, result_base, table))
    else:
        gui_start(number, original_base, result_base, table)


if __name__ == '__main__':
    process()

MainWindow.py

# -*- coding: utf-8 -*-

# Form implementation generated from reading ui file '.\MainWindow.ui'
#
# Created by: PyQt5 UI code generator 5.14.1
#
# WARNING! All changes made in this file will be lost!


from PyQt5 import QtCore, QtGui, QtWidgets


class Ui_MainWindow(object):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(294, 222)
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.gridLayout = QtWidgets.QGridLayout(self.centralwidget)
        self.gridLayout.setObjectName("gridLayout")
        self.formLayout = QtWidgets.QFormLayout()
        self.formLayout.setObjectName("formLayout")
        self.originalNumberLabel = QtWidgets.QLabel(self.centralwidget)
        self.originalNumberLabel.setObjectName("originalNumberLabel")
        self.formLayout.setWidget(0, QtWidgets.QFormLayout.LabelRole, self.originalNumberLabel)
        self.originalNumberLineEdit = QtWidgets.QLineEdit(self.centralwidget)
        self.originalNumberLineEdit.setObjectName("originalNumberLineEdit")
        self.formLayout.setWidget(0, QtWidgets.QFormLayout.FieldRole, self.originalNumberLineEdit)
        self.originalBaseLabel = QtWidgets.QLabel(self.centralwidget)
        self.originalBaseLabel.setObjectName("originalBaseLabel")
        self.formLayout.setWidget(1, QtWidgets.QFormLayout.LabelRole, self.originalBaseLabel)
        self.originalBaseLineEdit = QtWidgets.QLineEdit(self.centralwidget)
        self.originalBaseLineEdit.setObjectName("originalBaseLineEdit")
        self.formLayout.setWidget(1, QtWidgets.QFormLayout.FieldRole, self.originalBaseLineEdit)
        self.resultBaseLabel = QtWidgets.QLabel(self.centralwidget)
        self.resultBaseLabel.setObjectName("resultBaseLabel")
        self.formLayout.setWidget(2, QtWidgets.QFormLayout.LabelRole, self.resultBaseLabel)
        self.resultBaseLineEdit = QtWidgets.QLineEdit(self.centralwidget)
        self.resultBaseLineEdit.setObjectName("resultBaseLineEdit")
        self.formLayout.setWidget(2, QtWidgets.QFormLayout.FieldRole, self.resultBaseLineEdit)
        self.resultNumberLabel = QtWidgets.QLabel(self.centralwidget)
        self.resultNumberLabel.setObjectName("resultNumberLabel")
        self.formLayout.setWidget(3, QtWidgets.QFormLayout.LabelRole, self.resultNumberLabel)
        self.resultNumberLineEdit = QtWidgets.QLineEdit(self.centralwidget)
        self.resultNumberLineEdit.setObjectName("resultNumberLineEdit")
        self.formLayout.setWidget(3, QtWidgets.QFormLayout.FieldRole, self.resultNumberLineEdit)
        self.usingTableLabel = QtWidgets.QLabel(self.centralwidget)
        self.usingTableLabel.setObjectName("usingTableLabel")
        self.formLayout.setWidget(4, QtWidgets.QFormLayout.LabelRole, self.usingTableLabel)
        self.usingTableCheckBox = QtWidgets.QCheckBox(self.centralwidget)
        self.usingTableCheckBox.setObjectName("usingTableCheckBox")
        self.formLayout.setWidget(4, QtWidgets.QFormLayout.FieldRole, self.usingTableCheckBox)
        self.tableLabel = QtWidgets.QLabel(self.centralwidget)
        self.tableLabel.setEnabled(False)
        self.tableLabel.setObjectName("tableLabel")
        self.formLayout.setWidget(5, QtWidgets.QFormLayout.LabelRole, self.tableLabel)
        self.tableLineEdit = QtWidgets.QLineEdit(self.centralwidget)
        self.tableLineEdit.setEnabled(False)
        self.tableLineEdit.setObjectName("tableLineEdit")
        self.formLayout.setWidget(5, QtWidgets.QFormLayout.FieldRole, self.tableLineEdit)
        self.gridLayout.addLayout(self.formLayout, 0, 0, 1, 1)
        MainWindow.setCentralWidget(self.centralwidget)
        self.menubar = QtWidgets.QMenuBar(MainWindow)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 294, 26))
        self.menubar.setObjectName("menubar")
        MainWindow.setMenuBar(self.menubar)
        self.statusbar = QtWidgets.QStatusBar(MainWindow)
        self.statusbar.setObjectName("statusbar")
        MainWindow.setStatusBar(self.statusbar)

        self.retranslateUi(MainWindow)
        self.usingTableCheckBox.clicked['bool'].connect(self.tableLabel.setEnabled)
        self.originalBaseLineEdit.textChanged['QString'].connect(self.originalNumberLineEdit.clear)
        self.originalBaseLineEdit.textChanged['QString'].connect(self.resultNumberLineEdit.clear)
        self.resultBaseLineEdit.textChanged['QString'].connect(self.originalNumberLineEdit.clear)
        self.resultBaseLineEdit.textChanged['QString'].connect(self.resultNumberLineEdit.clear)
        self.usingTableCheckBox.clicked['bool'].connect(self.tableLineEdit.setEnabled)
        self.tableLineEdit.textChanged['QString'].connect(self.originalNumberLineEdit.clear)
        self.tableLineEdit.textChanged['QString'].connect(self.resultNumberLineEdit.clear)
        self.usingTableCheckBox.toggled['bool'].connect(self.originalNumberLineEdit.clear)
        self.usingTableCheckBox.toggled['bool'].connect(self.resultNumberLineEdit.clear)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "Base Converter"))
        self.originalNumberLabel.setText(_translate("MainWindow", "Original Number"))
        self.originalBaseLabel.setText(_translate("MainWindow", "Original Base"))
        self.resultBaseLabel.setText(_translate("MainWindow", "Result Base"))
        self.resultNumberLabel.setText(_translate("MainWindow", "Result Number"))
        self.usingTableLabel.setText(_translate("MainWindow", "Using Table"))
        self.tableLabel.setText(_translate("MainWindow", "Table"))

MainWindow.ui

<?xml version="1.0" encoding="UTF-8"?>
<ui version="4.0">
 <class>MainWindow</class>
 <widget class="QMainWindow" name="MainWindow">
  <property name="geometry">
   <rect>
    <x>0</x>
    <y>0</y>
    <width>294</width>
    <height>222</height>
   </rect>
  </property>
  <property name="windowTitle">
   <string>Base Converter</string>
  </property>
  <widget class="QWidget" name="centralwidget">
   <layout class="QGridLayout" name="gridLayout">
    <item row="0" column="0">
     <layout class="QFormLayout" name="formLayout">
      <item row="0" column="0">
       <widget class="QLabel" name="originalNumberLabel">
        <property name="text">
         <string>Original Number</string>
        </property>
       </widget>
      </item>
      <item row="0" column="1">
       <widget class="QLineEdit" name="originalNumberLineEdit"/>
      </item>
      <item row="1" column="0">
       <widget class="QLabel" name="originalBaseLabel">
        <property name="text">
         <string>Original Base</string>
        </property>
       </widget>
      </item>
      <item row="1" column="1">
       <widget class="QLineEdit" name="originalBaseLineEdit"/>
      </item>
      <item row="2" column="0">
       <widget class="QLabel" name="resultBaseLabel">
        <property name="text">
         <string>Result Base</string>
        </property>
       </widget>
      </item>
      <item row="2" column="1">
       <widget class="QLineEdit" name="resultBaseLineEdit"/>
      </item>
      <item row="3" column="0">
       <widget class="QLabel" name="resultNumberLabel">
        <property name="text">
         <string>Result Number</string>
        </property>
       </widget>
      </item>
      <item row="3" column="1">
       <widget class="QLineEdit" name="resultNumberLineEdit"/>
      </item>
      <item row="4" column="0">
       <widget class="QLabel" name="usingTableLabel">
        <property name="text">
         <string>Using Table</string>
        </property>
       </widget>
      </item>
      <item row="4" column="1">
       <widget class="QCheckBox" name="usingTableCheckBox"/>
      </item>
      <item row="5" column="0">
       <widget class="QLabel" name="tableLabel">
        <property name="enabled">
         <bool>false</bool>
        </property>
        <property name="text">
         <string>Table</string>
        </property>
       </widget>
      </item>
      <item row="5" column="1">
       <widget class="QLineEdit" name="tableLineEdit">
        <property name="enabled">
         <bool>false</bool>
        </property>
       </widget>
      </item>
     </layout>
    </item>
   </layout>
  </widget>
  <widget class="QMenuBar" name="menubar">
   <property name="geometry">
    <rect>
     <x>0</x>
     <y>0</y>
     <width>294</width>
     <height>26</height>
    </rect>
   </property>
  </widget>
  <widget class="QStatusBar" name="statusbar"/>
 </widget>
 <resources/>
 <connections>
  <connection>
   <sender>usingTableCheckBox</sender>
   <signal>clicked(bool)</signal>
   <receiver>tableLabel</receiver>
   <slot>setEnabled(bool)</slot>
   <hints>
    <hint type="sourcelabel">
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    </hint>
    <hint type="destinationlabel">
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  </connection>
  <connection>
   <sender>originalBaseLineEdit</sender>
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   <slot>clear()</slot>
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  <connection>
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  </connection>
  <connection>
   <sender>tableLineEdit</sender>
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   <slot>clear()</slot>
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 </connections>
</ui>