Added binary shifts and twos complement functions to bit manipulation (#4068)

* Added binary shifts and twos complement functions to bit manipulation package

* Fixed problem representing 0 wrong

* More testing

* Fixed problems

* Fixed formatting

* More format fixes

* Format fixes

* Fixed docstrings and added url

* Minor change to url

bit_manipulation/binary_shifts.py

@@ -0,0 +1,111 @@
+# Information on binary shifts:
+# https://docs.python.org/3/library/stdtypes.html#bitwise-operations-on-integer-types
+# https://www.interviewcake.com/concept/java/bit-shift
+
+
+def logical_left_shift(number: int, shift_amount: int) -> str:
+    """
+    Take in 2 positive integers.
+    'number' is the integer to be logically left shifted 'shift_amount' times.
+    i.e. (number << shift_amount)
+    Return the shifted binary representation.
+
+    >>> logical_left_shift(0, 1)
+    '0b00'
+    >>> logical_left_shift(1, 1)
+    '0b10'
+    >>> logical_left_shift(1, 5)
+    '0b100000'
+    >>> logical_left_shift(17, 2)
+    '0b1000100'
+    >>> logical_left_shift(1983, 4)
+    '0b111101111110000'
+    >>> logical_left_shift(1, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: both inputs must be positive integers
+    """
+    if number < 0 or shift_amount < 0:
+        raise ValueError("both inputs must be positive integers")
+
+    binary_number = str(bin(number))
+    binary_number += "0" * shift_amount
+    return binary_number
+
+
+def logical_right_shift(number: int, shift_amount: int) -> str:
+    """
+    Take in positive 2 integers.
+    'number' is the integer to be logically right shifted 'shift_amount' times.
+    i.e. (number >>> shift_amount)
+    Return the shifted binary representation.
+
+    >>> logical_right_shift(0, 1)
+    '0b0'
+    >>> logical_right_shift(1, 1)
+    '0b0'
+    >>> logical_right_shift(1, 5)
+    '0b0'
+    >>> logical_right_shift(17, 2)
+    '0b100'
+    >>> logical_right_shift(1983, 4)
+    '0b1111011'
+    >>> logical_right_shift(1, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: both inputs must be positive integers
+    """
+    if number < 0 or shift_amount < 0:
+        raise ValueError("both inputs must be positive integers")
+
+    binary_number = str(bin(number))[2:]
+    if shift_amount >= len(binary_number):
+        return "0b0"
+    shifted_binary_number = binary_number[: len(binary_number) - shift_amount]
+    return "0b" + shifted_binary_number
+
+
+def arithmetic_right_shift(number: int, shift_amount: int) -> str:
+    """
+    Take in 2 integers.
+    'number' is the integer to be arithmetically right shifted 'shift_amount' times.
+    i.e. (number >> shift_amount)
+    Return the shifted binary representation.
+
+    >>> arithmetic_right_shift(0, 1)
+    '0b00'
+    >>> arithmetic_right_shift(1, 1)
+    '0b00'
+    >>> arithmetic_right_shift(-1, 1)
+    '0b11'
+    >>> arithmetic_right_shift(17, 2)
+    '0b000100'
+    >>> arithmetic_right_shift(-17, 2)
+    '0b111011'
+    >>> arithmetic_right_shift(-1983, 4)
+    '0b111110000100'
+    """
+    if number >= 0:  # Get binary representation of positive number
+        binary_number = "0" + str(bin(number)).strip("-")[2:]
+    else:  # Get binary (2's complement) representation of negative number
+        binary_number_length = len(bin(number)[3:])  # Find 2's complement of number
+        binary_number = bin(abs(number) - (1 << binary_number_length))[3:]
+        binary_number = (
+            ("1" + "0" * (binary_number_length - len(binary_number)) + binary_number)
+            if number < 0
+            else "0"
+        )
+
+    if shift_amount >= len(binary_number):
+        return "0b" + binary_number[0] * len(binary_number)
+    return (
+        "0b"
+        + binary_number[0] * shift_amount
+        + binary_number[: len(binary_number) - shift_amount]
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

bit_manipulation/binary_twos_complement.py

@@ -0,0 +1,43 @@
+# Information on 2's complement: https://en.wikipedia.org/wiki/Two%27s_complement
+
+
+def twos_complement(number: int) -> str:
+    """
+    Take in a negative integer 'number'.
+    Return the two's complement representation of 'number'.
+
+    >>> twos_complement(0)
+    '0b0'
+    >>> twos_complement(-1)
+    '0b11'
+    >>> twos_complement(-5)
+    '0b1011'
+    >>> twos_complement(-17)
+    '0b101111'
+    >>> twos_complement(-207)
+    '0b100110001'
+    >>> twos_complement(1)
+    Traceback (most recent call last):
+        ...
+    ValueError: input must be a negative integer
+    """
+    if number > 0:
+        raise ValueError("input must be a negative integer")
+    binary_number_length = len(bin(number)[3:])
+    twos_complement_number = bin(abs(number) - (1 << binary_number_length))[3:]
+    twos_complement_number = (
+        (
+            "1"
+            + "0" * (binary_number_length - len(twos_complement_number))
+            + twos_complement_number
+        )
+        if number < 0
+        else "0"
+    )
+    return "0b" + twos_complement_number
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()