★ number systems

denary (0 - 9): 10 digits, the one we commonly use

binary (0 and 1): 2 digits, the only one used to store data on computers

hexadecimal (0 - 9, A - F): 16 digits, easiest way

binary conversions: n-bits is $2^n$ possible combinations

• bit – a 0 or a 1 (smallest unit of data a computer can use)

• 4 bits – nibble

• 8 bits – a byte

• 1000 bits – 1 kilobyte (KB)

• 1000 KB – 1 megabyte (MB)

• 1000 GB – 1 gigabyte (GB)

• 1000 GB – 1 terabyte (TB)

• 1024 bits – 1 kibibyte (1KiB)

• 1024 KiB – 1 mebibyte (MiB)

• 1024 MiB – 1 gibibyte (GiB)

• 1024 GiB – 1 tebibyte (TiB)

★ binary addition

rules of binary addition:

• $0 + 0 = 0$
• $0 + 1 = 1$
• $1 + 1 = 0$, carry $1$
• $1 + 1 + 1 = 1$, carry $1$

overflow: this occurs when there are not enough bits to store the data (the computer does not give an error message)

★ signed binaries

signed binaries: often used to represent negative numbers in binary

the leftmost bit is called the most significant bit (MSB)

the rightmost bit is called the least significant bit (LSB)

☆ sign & magnitude