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What is the set of natural numbers and its notation?
The set of natural numbers, ℕ, includes all positive integers starting from 0.
ℕ = { 0, 1, 2, 3, 4, … }
What is the set of integer numbers and its notation?
The set of integer numbers, ℤ, includes all positive and negative integers.
ℤ = { …, -3, -2, -1, 0, 1, 2, 3, … }
What is the set of rational numbers and its notation?
The set of rational numbers, ℚ, includes all numbers that can be expressed as fractions
ℚ = { …, -2, -4/3, 0, 1/100, … }
What is the set of irrational numbers?
The set of irrational numbers includes all real numbers that cannot be expressed as fractions.
{ …, π, √2, e, … }
What is the set of real numbers and its notation?
The set of real numbers, ℝ, includes all rational and irrational numbers
What are ordinal numbers used for?
Ordinal numbers describe the order in which elements appear in a set. Example: In {apple, banana, clementine}, 'clementine' is the third item.
Why are natural numbers used for counting?
Natural numbers are used for counting because they are discrete and relate to physically countable objects.
Why are real numbers used for measurement?
Real numbers are used for measurement because they are continuous and can be expressed in flexible terms.
Why is base 10 used and how is it notated?
Base 10, or decimal, is used because humans typically have 10 fingers. Decimal numbers can be written with the number 10 as a subscript; e.g., 4310
Why is base 2 used in computer systems and how is it notated?
Base 2, or binary, is used because computer systems are based on on/off circuits. Binary numbers can be written with the number 2 as a subscript; e.g., 0010 1011.
Why is base 16 used and how is it notated?
Base 16, or hexadecimal, is used as a shorthand for binary. It uses digits 0-9 and letters A-F. Hexadecimal numbers can be written with the number 16 as a subscript; e.g., 2B16.
What are the advantages of using hexadecimal?
Hexadecimal is easier to recall and less error-prone than binary. Each hexadecimal digit represents four binary digits, reducing length and improving readability.
How do you convert a decimal number to binary?
By repeatedly removing the largest possible power of 2 from the most significant bit to the least significant bit.
How do you convert a binary number to decimal?
Multiply each binary digit by its place value (powers of 2) and sum the results.
How do you convert binary to hexadecimal?
Group the binary digits in blocks of four and convert each block to its hexadecimal equivalent.
How do you convert hexadecimal to binary?
Expand each hexadecimal digit to its four-digit binary equivalent
F316 = 1111 00112
How do you convert a decimal number to hexadecimal directly?
Divide the decimal number by 16 and represent the division and remainder in hexadecimal.
17310 = 1010 11012 = AD16
What is a bit?
A single binary digit, referred to as a bit, can take the value of 0 or 1.
What is a byte?
A byte consists of eight binary digits (bits).
How many unique combinations are possible with n bits?
The number of unique combinations of values within a binary value is calculated using the formula 2n, where n is the number of bits
For a 2-bit binary value ( 𝑛 = 2 ): 22 = 4 There are 4 unique combinations: 00, 01, 10, and 11.
For a 3-bit binary value ( 𝑛 = 3): 23 = 8 There are 8 unique combinations: 000, 001, 010, 011, 100, 101, 110, and 111.
What are the decimal prefixes for binary data
The decimal prefixes for binary data are:
10^3 bytes = 1 kilobyte (kB)
10^6 bytes = 1 megabyte (MB)
10^9 bytes = 1 gigabyte (GB)
10^12 bytes = 1 terabyte (TB)
How do decimal and binary prefixes differ?
Decimal prefixes are based on powers of 10, while binary prefixes are based on powers of 2. For example:
1000 bytes=1 kB (decimal) vs. 1024 bytes = 1 KB (binary)
1000 kB=1 MB (decimal) vs. 1024 KiB = 1 MB (binary)
What is the decimal and binary prefix equivalent for 1 gigabyte?
Decimal: 1000 MB = 1 GB 1000 MB=1 GB
Binary: 1024 MB = 1 GB 1024 MB=1 GB
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