课 5, 主题 1

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bitwise-operations

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Binary shifts

What are binary shifts?

A binary shift is an operation that moves all the bits in a binary number left or right by a certain number of positions
Often used in programming and computer systems for fast multiplication or division by powers of 2, or for manipulating individual bits
There are three main types of binary shift:
- Logical
- Arithmetic
- Cyclic

Logical

Moves bits left or right and fills the gap with 0s
Used for unsigned binary numbers or raw bit manipulation

Direction	What happens
Left	All bits shift left, a `0` fills the rightmost bit
Right	All bits shift right, a `0` fills the leftmost bit

Left

The following number is shifted by two places to the left

Step	128	64	32	16	8	4	2	1
Original	0	0	0	0	1	1	1	0
Left shift by 2	0	0	1	1	1	0	0	0

Original number: 0000 1110 = 14
Left shift (2) result: 0011 1000 = 56
Each left shift has doubled the number:
- Original value = 14
- Left shift 1 – Doubled the number to 28
- Left shift 2 – Doubled the number to 56

Right

The following number is shifted by three places to the right

Step	128	64	32	16	8	4	2	1
Original	1	1	0	0	1	0	0	0
Right shift by 3	0	0	0	1	1	0	0	1

Original number: 1100 1000 = 200
Right shift (3) result: 0001 1001 = 25
Each right shift has halved the number:
- Original value = 200
- Right shift 1 – Halved the number to 100
- Right shift 2 – Halved the number to 50
- Right shift 3 – Halved the number to 25

Arithmetic

Moves bits, but preserves the sign bit (used for signed binary numbers in two’s complement)

Direction	What happens
Left	Same as logical left (shift left, 0 in)
Right	Shift right, copy the sign bit (MSB) into the new leftmost bit

Right

The following number is shifted by three places to the right

Step	128	64	32	16	8	4	2	1
Original	1	1	1	0	1	0	0	0
Right shift by 3	1	1	1	1	1	0	1	0

Original number: 1110 1000 = −24
Right shift (3) result: 1111 1010 = −6
Each arithmetic right shift divides the number by 2, rounding towards negative infinity (preserving the sign bit)
- Original value = −24
- Right shift 1 → 1111 0100 = −12
- Right shift 2 → 1111 1010 = −6
- Right shift 3 → 1111 1101 = −3

Cyclic

Rotates the bits around, nothing is lost, no 0s added
The bit that falls off one end is reused at the other end

Direction	What happens
Left	Leftmost bit moves to the rightmost position
Right	Rightmost bit moves to the leftmost position

The following number is shifted by three places to the left and right

Left and Right

Step	128	64	32	16	8	4	2	1
Original	1	0	1	1	0	0	0	1
Cyclic left (×3)	1	0	0	0	1	1	0	1
Cyclic right (×3)	0	0	1	1	0	0	1	0

The 3 leftmost bits 101 wrap around to the right side
The 3 rightmost bits 001 wrap around to the left side
Original: 1011 0001 = 177
Cyclic left (3): 1000 1101 = 141
Cyclic right (3): 0011 0010 = 50

Shift type	Left shift	Right shift	Used for
Logical Shift	Shift bits left, fill with `0`	Shift bits right, fill with `0`	Unsigned numbers, raw bits
Arithmetic Shift	Same as logical left	Shift bits right, preserve sign bit	Signed numbers (two’s complement)
Cyclic Shift	Rotate bits left (no loss)	Rotate bits right (no loss)	Bit rotation, encryption, checksums

Device control & bit masking

What is device control?

In computer systems and embedded devices, each bit in a byte can be used to represent the state of a device or feature (e.g. turning a light on, checking if a sensor is active, or flagging an error)
You can control or monitor these bits using bitwise operations and bit masking

What is bit masking?

Bit masking uses binary patterns (masks) to test, set, clear, or toggle specific bits without affecting the others

Bitwise AND operation (&)

Used to test if a specific bit is set to 1
Only returns 1 when both the binary value and the mask have 1 in the same position
Useful for checking the status of a device

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