Bitwise math/Shift and rotate

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Each of these operations can occur either to the right or to the left. Examples will use nibbles as operands (4 bits or 0.5 bytes).

Logical Shifts

For logical shifts, the bytes are assumed to be in big endian.

Using A or 1010 as an example:

Example: A shifted left by 1 = 4

Operation	Hexadecimal	Binary	comment
Left Shift	A 1	1010 0001	shifted to the left once, the 1 at the beginning gets shifted off, thus the binary value becomes 0100, or 4 in hexadecimal.
=	4	0100	The end value 0 is always used to replace the residual numbers.

Example: A shifted left by 2 = 8

Operation	Hexadecimal	Binary	comment
Left Shift	A 2	1010 0001	The first `10' is shifted off and the remaining two placeholders get zeroed out.
=	8	1000	The end value 0 is always used to replace the residual numbers.

Example: A shifted right by 1 = 5

Operation	Hexadecimal	Binary	comment
Right Shift	A 1	1010 0101	a single shift to the right is division by two for even numbers.
=	5	0101	The end value 0 is always used to replace the residual numbers.

If 'A' is shifted to the right twice it goes from 1010 to 0010

Operation	Hexadecimal	Binary	comment
Right Shift	A 2	1010 0001	shifted to the right twice, the one at the beginning gets shifted to the 2nd digit and the one in the 2nd digit place gets shifted off, thus the binary value becomes 0010, or 2 in hexadecimal.
=	2	0010	The end value 0 is always used to replace the residual numbers.

At this point, understanding should be emerging into real hacking and cryptography. If understanding is not attained regarding this knowledge, further extension topics will prove difficult. Thus, it is considered a baseline knowledge.

Exercises:

1) Solve for B left shift one

Operation	Hexadecimal	Binary
Left Shift One	B 1	"(B in Binary)" 0001
=	"??"	"???"

2) Solve for F right shift three

Operation	Hexadecimal	Binary
Right Shift three	F 3	"(F in Binary)" 0011
=	"??"	"???"

Answers:

1) 0110 or 6.

Operation	Hexadecimal	Binary
Left Shift One	B 1	1011 0001
=	"6"	"0110"

2) 0001 or 1.

Operation	Hexadecimal	Binary
Right Shift three	F 3	1110 0011
=	0001	1