Bits and Bytes

1. Bit representation in ordinal data types

Every bit has corresponding value in a ordinal data type

BIT_0 -> 1
BIT_1 -> 2
BIT_2 -> 4
BIT_3 -> 8
BIT_4 -> 16
BIT_5 -> 32
BIT_6 -> 64
BIT_7 -> 128

BIT_n -> 2^n

2. How to check if a bit is set

bitN = (value & BIT_N) == BIT_N

3. How to set a bit

value|= BIT_N

4. How to unset/toggle a bit

value~= BIT_N

5. Most/least significant bit

MSB                   LSB
7 6 5 4 3 2 1 0

the most significant bit in a byte is BIT_7 with a value of 128
the least significant bit in a byte is BIT_0 with a value of 1

6. Shifting

int<<=1

will multiply a int by 2 by moving the bits 1 bit left in direction to the most significant bit

int>>=1

will divide a int by 2 by moving the bits 1 bit to right in direction to the least significant bit

7. What else can you do

mask more than one bit

byte = int & 0xFF

will return only the first 8 bit (sum of BIT_0 … BIT_7 = 0xFF) from an integer

combined mask and shifting

byte0ofint = int & 0xFF
byte1ofint = (int & (0xFF << 8)) >> 8
byte2ofint = (int & (0xFF << 16)) >> 16
byte3ofint = (int & (0xFF << 24)) >> 24

8. Byte order

each cpu stores ordinal data types bigger than one byte in a specific byte order

intel: little endian byte order begins with LSB byte
powerpc: big endian byte order begins with MSB byte
arm: can do both as far as i know

so whenever you store and read ordinal data types bigger than a byte binary you should care about byte order

9. Why?

  • you need most likely work with bits and bytes when doing
    • hardware related programming
    • network programming
    • other stuff
      • e.g. you can implement sets using bits

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