diff --git a/exceptions.py b/exceptions.py
new file mode 100644
index 0000000..3a45308
--- /dev/null
+++ b/exceptions.py
@@ -0,0 +1,48 @@
+class calculatorerror(Exception):
+    def __init__(self, msg="calculator error"):
+        self.msg = msg
+        super().__init__(self.msg)
+
+class invalidinputerror(calculatorerror):
+    def __init__(self, msg="invalid input"):
+        super().__init__(msg)
+
+class zerodenominatorerror(calculatorerror):
+    def __init__(self, msg="denominator cannot be zero"):
+        super().__init__(msg)
+
+class invalidfractionerror(calculatorerror):
+    def __init__(self, msg="invalid fraction format"):
+        super().__init__(msg)
+
+class invalidcomplexerror(calculatorerror):
+    def __init__(self, msg="invalid complex number"):
+        super().__init__(msg)
+
+class invalidbinaryerror(calculatorerror):
+    def __init__(self, msg="invalid binary number"):
+        super().__init__(msg)
+
+class invalidoctalerror(calculatorerror):
+    def __init__(self, msg="invalid octal number"):
+        super().__init__(msg)
+
+class invalidhexerror(calculatorerror):
+    def __init__(self, msg="invalid hex number"):
+        super().__init__(msg)
+
+class invalidseterror(calculatorerror):
+    def __init__(self, msg="invalid set format"):
+        super().__init__(msg)
+
+class invalidmatrixerror(calculatorerror):
+    def __init__(self, msg="invalid matrix format"):
+        super().__init__(msg)
+
+class dimensionmismatcherror(calculatorerror):
+    def __init__(self, msg="matrix dimensions dont match"):
+        super().__init__(msg)
+
+class undefinedoperationerror(calculatorerror):
+    def __init__(self, msg="operation is undefined"):
+        super().__init__(msg)
diff --git a/fraction.py b/fraction.py
new file mode 100644
index 0000000..f15c0ec
--- /dev/null
+++ b/fraction.py
@@ -0,0 +1,74 @@
+import math
+from exceptions import zerodenominatorerror, invalidfractionerror
+
+
+def parse_frac(s):
+    s = s.strip()
+    if '/' in s:
+        parts = s.split('/')
+        if len(parts) != 2:
+            raise invalidfractionerror(f"bad fraction: '{s}'")
+        try:
+            num = int(parts[0].strip())
+            den = int(parts[1].strip())
+        except ValueError:
+            raise invalidfractionerror(f"bad fraction: '{s}'")
+    else:
+        try:
+            num = int(s)
+            den = 1
+        except ValueError:
+            raise invalidfractionerror(f"bad fraction: '{s}'")
+    if den == 0:
+        raise zerodenominatorerror("denominator is zero")
+    return num, den
+
+
+def simplify(num, den):
+    if num == 0:
+        return 0, 1
+    if den < 0:
+        num, den = -num, -den
+    g = math.gcd(abs(num), abs(den))
+    return num // g, den // g
+
+
+def format_frac(num, den):
+    num, den = simplify(num, den)
+    if den == 1:
+        return str(num)
+    return f"{num}/{den}"
+
+
+def add_fraction(a, b):
+    n1, d1 = parse_frac(a)
+    n2, d2 = parse_frac(b)
+    num = n1 * d2 + n2 * d1
+    den = d1 * d2
+    return format_frac(num, den)
+
+
+def sub_fraction(a, b):
+    n1, d1 = parse_frac(a)
+    n2, d2 = parse_frac(b)
+    num = n1 * d2 - n2 * d1
+    den = d1 * d2
+    return format_frac(num, den)
+
+
+def mul_fraction(a, b):
+    n1, d1 = parse_frac(a)
+    n2, d2 = parse_frac(b)
+    num = n1 * n2
+    den = d1 * d2
+    return format_frac(num, den)
+
+
+def div_fraction(a, b):
+    n1, d1 = parse_frac(a)
+    n2, d2 = parse_frac(b)
+    if n2 == 0:
+        raise zerodenominatorerror("cant divide by zero fraction")
+    num = n1 * d2
+    den = d1 * n2
+    return format_frac(num, den)
diff --git a/hex.py b/hex.py
new file mode 100644
index 0000000..76cc935
--- /dev/null
+++ b/hex.py
@@ -0,0 +1,68 @@
+from exceptions import invalidhexerror
+
+
+def check_hex(h):
+    h = h.strip()
+    if not h:
+        raise invalidhexerror("empty hex string")
+    valid = set('0123456789ABCDEFabcdef')
+    for ch in h:
+        if ch not in valid:
+            raise invalidhexerror(f"invalid character: '{ch}'")
+
+
+def hex_to_decimal(h):
+    h = h.strip()
+    check_hex(h)
+    return str(int(h, 16))
+
+
+def decimal_to_hex(d):
+    num = int(d.strip())
+    if num < 0:
+        return '-' + hex(abs(num))[2:].upper()
+    return hex(num)[2:].upper()
+
+
+def hex_add(a, b):
+    a, b = a.strip(), b.strip()
+    check_hex(a)
+    check_hex(b)
+    res = int(a, 16) + int(b, 16)
+    return hex(res)[2:].upper()
+
+
+def hex_subtract(a, b):
+    a, b = a.strip(), b.strip()
+    check_hex(a)
+    check_hex(b)
+    res = int(a, 16) - int(b, 16)
+    if res < 0:
+        return '-' + hex(abs(res))[2:].upper()
+    return hex(res)[2:].upper()
+
+
+def hex_multiply(a, b):
+    a, b = a.strip(), b.strip()
+    check_hex(a)
+    check_hex(b)
+    res = int(a, 16) * int(b, 16)
+    return hex(res)[2:].upper()
+
+
+def fifteens_complement(h):
+    h = h.strip()
+    check_hex(h)
+    result = []
+    for ch in h.upper():
+        val = int(ch, 16)
+        result.append(hex(15 - val)[2:].upper())
+    return ''.join(result)
+
+
+def sixteens_complement(h):
+    h = h.strip()
+    check_hex(h)
+    fifteens = fifteens_complement(h)
+    res = int(fifteens, 16) + 1
+    return hex(res)[2:].upper()
diff --git a/test_fraction.py b/test_fraction.py
new file mode 100644
index 0000000..b7e9380
--- /dev/null
+++ b/test_fraction.py
@@ -0,0 +1,68 @@
+import unittest
+from fraction import add_fraction, sub_fraction, mul_fraction, div_fraction
+from exceptions import zerodenominatorerror, invalidfractionerror
+
+
+class testfraction(unittest.TestCase):
+
+    def test_fraction_add(self):
+        self.assertEqual(add_fraction('1/2', '1/4'), '3/4')
+
+    def test_fraction_add_same_denom(self):
+        self.assertEqual(add_fraction('1/5', '2/5'), '3/5')
+
+    def test_fraction_add_simplify(self):
+        self.assertEqual(add_fraction('1/4', '1/4'), '1/2')
+
+    def test_fraction_add_whole_result(self):
+        self.assertEqual(add_fraction('1/2', '1/2'), '1')
+
+    def test_fraction_add_negative(self):
+        self.assertEqual(add_fraction('-1/2', '1/4'), '-1/4')
+
+    def test_fraction_add_zero(self):
+        self.assertEqual(add_fraction('0/5', '3/7'), '3/7')
+
+    def test_fraction_sub(self):
+        self.assertEqual(sub_fraction('3/4', '1/4'), '1/2')
+
+    def test_fraction_sub_negative_result(self):
+        self.assertEqual(sub_fraction('1/4', '3/4'), '-1/2')
+
+    def test_fraction_sub_same(self):
+        self.assertEqual(sub_fraction('3/5', '3/5'), '0')
+
+    def test_fraction_mul(self):
+        self.assertEqual(mul_fraction('2/3', '3/4'), '1/2')
+
+    def test_fraction_mul_by_zero(self):
+        self.assertEqual(mul_fraction('2/3', '0/5'), '0')
+
+    def test_fraction_mul_whole_number(self):
+        self.assertEqual(mul_fraction('1/2', '2'), '1')
+
+    def test_fraction_div(self):
+        self.assertEqual(div_fraction('1/2', '1/4'), '2')
+
+    def test_fraction_div_result_fraction(self):
+        self.assertEqual(div_fraction('1/3', '2/3'), '1/2')
+
+    def test_fraction_div_by_zero(self):
+        with self.assertRaises(zerodenominatorerror):
+            div_fraction('1/2', '0/3')
+
+    def test_fraction_zero_denominator(self):
+        with self.assertRaises(zerodenominatorerror):
+            add_fraction('1/0', '1/2')
+
+    def test_fraction_invalid_format(self):
+        with self.assertRaises(invalidfractionerror):
+            add_fraction('abc', '1/2')
+
+    def test_fraction_invalid_format_multiple_slashes(self):
+        with self.assertRaises(invalidfractionerror):
+            add_fraction('1/2/3', '1/2')
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/test_hex.py b/test_hex.py
new file mode 100644
index 0000000..3fc6563
--- /dev/null
+++ b/test_hex.py
@@ -0,0 +1,67 @@
+import unittest
+from hex import (
+    hex_to_decimal, decimal_to_hex, hex_add,
+    hex_subtract, hex_multiply, fifteens_complement, sixteens_complement
+)
+from exceptions import invalidhexerror
+
+
+class testhex(unittest.TestCase):
+
+    def test_hex_to_decimal(self):
+        self.assertEqual(hex_to_decimal('1A5'), '421')
+
+    def test_hex_to_decimal_zero(self):
+        self.assertEqual(hex_to_decimal('0'), '0')
+
+    def test_hex_to_decimal_single(self):
+        self.assertEqual(hex_to_decimal('F'), '15')
+
+    def test_hex_to_decimal_lowercase(self):
+        self.assertEqual(hex_to_decimal('ff'), '255')
+
+    def test_decimal_to_hex(self):
+        self.assertEqual(decimal_to_hex('243'), 'F3')
+
+    def test_decimal_to_hex_zero(self):
+        self.assertEqual(decimal_to_hex('0'), '0')
+
+    def test_decimal_to_hex_255(self):
+        self.assertEqual(decimal_to_hex('255'), 'FF')
+
+    def test_hex_add(self):
+        self.assertEqual(hex_add('1A', '0F'), '29')
+
+    def test_hex_add_with_carry(self):
+        self.assertEqual(hex_add('FF', '1'), '100')
+
+    def test_hex_subtract(self):
+        self.assertEqual(hex_subtract('1A', '0F'), 'B')
+
+    def test_hex_multiply(self):
+        self.assertEqual(hex_multiply('A', '2'), '14')
+
+    def test_fifteens_complement(self):
+        self.assertEqual(fifteens_complement('1A5'), 'E5A')
+
+    def test_fifteens_complement_all_f(self):
+        self.assertEqual(fifteens_complement('FFF'), '000')
+
+    def test_sixteens_complement(self):
+        self.assertEqual(sixteens_complement('1A5'), 'E5B')
+
+    def test_invalid_hex_char(self):
+        with self.assertRaises(invalidhexerror):
+            hex_to_decimal('1G5')
+
+    def test_invalid_hex_special(self):
+        with self.assertRaises(invalidhexerror):
+            hex_to_decimal('12#')
+
+    def test_invalid_hex_empty(self):
+        with self.assertRaises(invalidhexerror):
+            hex_to_decimal('')
+
+
+if __name__ == "__main__":
+    unittest.main()