[AP CSP] number systems

base 10

base 10

decimal; 10 digits from 0 to 9

good at performing arithmetic on small to medium sized numbers

base 2

binary; 2 digits which are 0 and 1

computers use binary as their native language, representing all data & instructions; well suited for electronic devices bc it’s easy to represent using voltage levels

simplifies digital logic design & is the foundation of modern computer systems

why is understanding how to convert between decimal and binary important?

converting can optimize storage space + design more efficient data compression algorithms; form of digital literacy

logic error

mistake in the algorithm or program that causes it to behave incorrectly/unexpectedly

syntax error

mistake in the algorithm or program where the rules of the programming language are not followed

runtime error

mistake in the program that occurs during the execution of a program

overflow error

type of RUNTIME ERROR where programs try to use numbers outside of their fixed# of bits which limits the range of integer values it can represent

base 16

hexadecimal; 0-9 and then A-F

often used in computing as a more human friendly repres. of binary; each hexadecimal digit = 4 bits

commonly used in programming & debugging, esp. when dealing with memory address & low level data manipulation

base 8

octal; fewer applications today, historically used in early systems for simplifying hardware design and programming —> replaced by hexadecimal

compact repres. on binary; each octal digit = 3 bits

each segment of an IP address is an octal

hexadecimal pros

compact representation (useful for large binary numbers), alignment with memory addressing, representation of data patterns (digital design), representation of color !! , system programming (registers)