Number Systems and Data Representation

Question 1

defines how numbers are represented using symbols or digits and how arithmetic operations are performed on these numbers

Answer 1

Number System

Question 2

forms the basis for data representation, memory addressing, and low-level operations in computing devices

Answer 2

Number System

Question 3

mathematical notation for expressing numbers

Answer 3

Number System

Question 4

counting using fingers

Answer 4

decimal number system

Question 5

Base-10

Answer 5

decimal number system

Question 6

for computers-since flip flops

Answer 6

binary number system

Question 7

Base 2

Answer 7

binary number system

Question 8

to shorten long binary numbers

Answer 8

octal number system

Question 9

since data is stored in bytes

Answer 9

hexadecimal number system

Question 10

Base-8

Answer 10

octal number system

Question 11

Base-16

Answer 11

hexadecimal number system

Question 12

most widely used number system in the world; most intuitive for everyday calculations

Answer 12

decimal number system

Question 13

What ten symbols does the decimal number system use to represent numbers?

Answer 13

0 to 9

Question 14

also referred to as radix

Answer 14

base

Question 15

indicates the number of unique digits (including 0) used to represent numbers in the system

Answer 15

base

Question 16

system for expressing numerals; position of digit indicates the power of the base that the digit must be multiplied by to determine its value

Answer 16

positional number system

Question 17

represents number in terms of 0 and 1 only

Answer 17

binary number system

Question 18

uses 16 symbols

Answer 18

hexadecimal number system

Question 19

what are the 16 symbols that the hexadecimal number systems use to represent numbers?

Answer 19

0-9, A-F

Question 20

often used in computing for its compact representation of binary data; commonly used in memory addresses, color codes (RGB), low-level programming

Answer 20

hexadecimal number system

Question 21

Conversion between Number Systems

Answer 21

Decimal to Binary, Binary to Decimal, Decimal to Hexadecimal, Hexadecimal to Decimal

Question 22

divide the decimal number by 2 repeatedly and note the remainders; reading the remainders from bottom to top gives the binary equivalent

Answer 22

Decimal to Binary

Question 23

multiply each binary digit by 2 raised to the corresponding position’s power and add them together

Answer 23

Binary to Decimal

Question 24

divide the decimal number by 16 repeatedly, noting both quotients and remainders; convert remainders greater than 9 to A-F for the hexadecimal representation

Answer 24

Decimal to Hexadecimal

Question 25

multiply each hexadecimal digit by 16 raised to the corresponding position’s power and add them together

Answer 25

Hexadecimal to Decimal

Question 26

Operations on Binary Numbers

Answer 26

Binary Addition, Binary Subtraction