Number Systems, Base Conversion, and Data Representation

Flashcards covering number classifications, base conversion systems (binary, decimal, hexadecimal), signal types, binary units, and storage measurement prefixes.

natural numbers

Natural numbers are positive whole numbers used for counting (including 0). Their mathematical notation is $\mathbb{N}$.

integer numbers

Integer numbers are positive or negative whole numbers (including 0), represented by the notation $\mathbb{Z}$. $\mathbb{Z}$ includes all of $\mathbb{N}$.

rational number

A rational number is any number that can be expressed as a ratio or fraction. Its notation $\mathbb{Q}$ includes all of $\mathbb{Z}$ and $\mathbb{N}$.

irrational numbers

Irrational numbers are numbers that cannot be expressed as a fraction and have a series of non-repeating digits.

real numbers

Real numbers represent any possible real world quantity expressed as a number. Their mathematical notation is $\mathbb{R}$, which includes $\mathbb{Q}$, $\mathbb{Z}$, and $\mathbb{N}$.

What is the function of ordinal numbers?

Ordinal numbers are used to describe the numerical positions of objects.

What are the key characteristics of Base 2 (Binary)?

Base 2 consists of 2 unique digits (0 & 1), where 0 represents off and 1 represents on. Its column weightings are multiplied by two / powers of two.

What are the key characteristics of Base 10 (Decimal\denary)?

Base 10 contains unique digits 0-9 and calculates values by multiplying column weightings by 10.

How does Base 16 (Hexadecimal) represent values from 0 to 15?

Base 16 uses 16 unique digits: the numbers 0-9 are used for values 0-9, and the letters A-F represent the numbers 10-15.

Why is hexadecimal used, and how does a single hexadecimal character relate to binary?

Hexadecimal is used as a convenient shorthand version of representing long binary numbers. A single hexadecimal character equals a sequence of 4 binary characters.

What is the binary and hexadecimal representation of decimal number 12?

Decimal 12 in binary is 00001100, which corresponds to Hex 0C.

What is the binary and hexadecimal representation of decimal number 24?

Decimal 24 in binary is 00011000, which corresponds to Hex 18.

How do analog signals and digital signals differ?

In analog signals, everything is represented by sinuous waves that progress slowly from one state to another. Digital signals switch instantaneously from on to off.

What is a bit, and why is binary beneficial in digital hardware?

A bit is the smallest possible unit (1 or 0, representing on or off). It is easy to build and less prone to errors compared to having additional states.

How many bits are contained in a nibble and a byte?

A nibble consists of 4 bits, and a byte consists of 8 bits (or 2 nibbles).

What are the decimal (powers of 10) measurements for storage prefixes?

1 KB = 1,000 bytes, 1 MB = 1,000,000 bytes, and 1 GB = 1,000,000,000 bytes.

What are the binary (powers of 2) measurements for storage prefixes?

1 KiB = 1,024 bytes, 1 MiB = 1,024 KiB, 1 GiB = 1,024 MiB, and 1 TiB = 1,024 GiB.

Which storage devices use units to describe capacity?

Computers use these units to describe the capacity of RAM, Hard drives, SSDs, and optical discs such as DVDs.