Number Systems and Data Representation Flashcards
defines how numbers are represented using symbols or digits and how arithmetic operations are performed on these numbers
Number System
forms the basis for data representation, memory addressing, and low-level operations in computing devices
Number System
mathematical notation for expressing numbers
Number System
counting using fingers
decimal number system
Base-10
decimal number system
for computers-since flip flops
binary number system
Base 2
binary number system
to shorten long binary numbers
octal number system
since data is stored in bytes
hexadecimal number system
Base-8
octal number system
Base-16
hexadecimal number system
most widely used number system in the world; most intuitive for everyday calculations
decimal number system
What ten symbols does the decimal number system use to represent numbers?
0 to 9
also referred to as radix
base
indicates the number of unique digits (including 0) used to represent numbers in the system
base
system for expressing numerals; position of digit indicates the power of the base that the digit must be multiplied by to determine its value
positional number system
represents number in terms of 0 and 1 only
binary number system
uses 16 symbols
hexadecimal number system
what are the 16 symbols that the hexadecimal number systems use to represent numbers?
0-9, A-F
often used in computing for its compact representation of binary data; commonly used in memory addresses, color codes (RGB), low-level programming
hexadecimal number system
Conversion between Number Systems
Decimal to Binary, Binary to Decimal, Decimal to Hexadecimal, Hexadecimal to Decimal
divide the decimal number by 2 repeatedly and note the remainders; reading the remainders from bottom to top gives the binary equivalent
Decimal to Binary
multiply each binary digit by 2 raised to the corresponding position’s power and add them together
Binary to Decimal
divide the decimal number by 16 repeatedly, noting both quotients and remainders; convert remainders greater than 9 to A-F for the hexadecimal representation
Decimal to Hexadecimal
multiply each hexadecimal digit by 16 raised to the corresponding position’s power and add them together
Hexadecimal to Decimal
Operations on Binary Numbers
Binary Addition, Binary Subtraction
