Step by Step solution about How to resolve the algorithm Bitwise operations step by step in the Mathematica/ Wolfram Language programming language

This Wolfram code snippet demonstrates various bitwise operations and bit manipulation techniques. Here's a detailed explanation of each operation:

Bit And (BitAnd[integer1, integer2]):

• Performs a bitwise AND operation on two integers (integer1 and integer2).
• Each bit in the result is set to 1 only if both corresponding bits in the input integers are 1.
• Otherwise, it is set to 0.

Bit Xor (BitXor[integer1, integer2]):

• Performs a bitwise XOR operation on two integers (integer1 and integer2).
• Each bit in the result is set to 1 if the corresponding bits in the input integers are different (one is 0 and the other is 1).
• Otherwise, it is set to 0.

Bit Or (BitOr[integer1, integer2]):

• Performs a bitwise OR operation on two integers (integer1 and integer2).
• Each bit in the result is set to 1 if at least one corresponding bit in the input integers is 1.
• Otherwise, it is set to 0.

Bit Not (BitNot[integer1]):

• Performs a bitwise NOT operation on an integer (integer1).
• Flips all the bits in the input integer, converting 0s to 1s and 1s to 0s.

Bit Shift Left (BitShiftLeft[integer1]):

• Shifts all the bits in the input integer (integer1) to the left by one position.
• The leftmost bit is shifted out and discarded, and a 0 is added to the right end.
• This is equivalent to multiplying the integer by 2.

Bit Shift Right (BitShiftRight[integer1]):

• Shifts all the bits in the input integer (integer1) to the right by one position.
• The rightmost bit is shifted out and discarded, and a 0 is added to the left end.
• This is equivalent to dividing the integer by 2 (integer division).

Rotate Digits Left (RotateLeft[IntegerDigits[integer1, 2]], 2]):

• Converts the input integer (integer1) to its binary representation (digits) using the IntegerDigits function.
• Rotates the binary digits left by one position using the RotateLeft function.
• Converts the rotated binary digits back to an integer using the FromDigits function with a base of 2.

Rotate Digits Right (RotateRight[IntegerDigits[integer1, 2]], 2]):

• Similar to rotating digits left, but it rotates the binary digits right by one position.

Right Arithmetic Shift (Prepend[Most[#], #[[1]]], 2] &[IntegerDigits[integer1, 2]]):

• Converts the input integer (integer1) to its binary representation using IntegerDigits.
• Performs a right arithmetic shift by removing the rightmost digit and prepending it to the list of digits.
• This is different from a bit shift right, as it preserves the sign bit in the case of negative integers.

Example: The final line of the code shows an example of bitwise XOR operation:

BitXor[3333, 5555, 7777, 9999]

This operation calculates the bitwise XOR of four integers (3333, 5555, 7777, and 9999) and returns the result as 8664.

(*and xor and or*)
BitAnd[integer1, integer2]
BitXor[integer1, integer2]
BitOr[integer1, integer2]

(*logical not*)
BitNot[integer1]

(*left and right shift*)
BitShiftLeft[integer1]
BitShiftRight[integer1]

(*rotate digits left and right*)
FromDigits[RotateLeft[IntegerDigits[integer1, 2]], 2]
FromDigits[RotateRight[IntegerDigits[integer1, 2]], 2]

(*right arithmetic shift*)
FromDigits[Prepend[Most[#], #[[1]]], 2] &[IntegerDigits[integer1, 2]]


BitXor[3333, 5555, 7777, 9999]


8664