Number Systems / Binary

Computer Science Dat rep

What letter is used to represent Natural numbers?

ℕ

What letter is used to represent Integers?

ℤ

What letter is used to represent Rational numbers?

ℚ

What is an irrational number?

An irrational number is a real number that cannot be expressed as a fraction of two integers, so it has infinite decimal places.

What is a rational number?

A number that can be expressed as a fraction or ratio.

What is a natural number?

A natural number is a whole, positive number

What is an integer?

A whole number that can be positive, negative, or zero, and does not include fractional or decimal parts.

What is an Order?

A number that represent the position of something in a list.

Give three Reasons Hexadecimal is used.

• Easier to read and remember than a string of binary digits

• Quicker to write / type

• Less chance of error than Binary (as binary is just 1’s and 0’)

• Takes up less space on a page than binary

How many values can be stored in 8 bits?

128 (2^8)

What’s the largest number that can be stored in 8 bits?

127 (2^8 - 1)

How many bits in a byte?

8

How many bytes in one mebibyte (as a power of 2)?

2^20

What does ASCII stand for?

American Standard Code for Information Interchange

How many bits does ASCII use?

8

How many bits does Unicode use?

16

Name Three Types of Error Detection

• Parity Bits

• Checksums

• Majority Voting

• Check Digits

Describe how parity bits work

Parity bits are used in error detection by adding an extra bit to a binary string to ensure the total number of 1s is even (even parity) or odd (odd parity). This allows the detection of single-bit errors during data transmission.

What might cause an error to slip through parity bits?

If multiple Bits were to flip

Give three examples of what might cause a transmission error

• Electrical Interference

• Power Surges

• Synchronization Issues

• Worn Cables / Connectors

How does majority voting work?

Each bit is sent 3 times and whatever number (1 or 0) is more common, that number is assumed to be true.

What is a drawback of majority voting?

It takes much longer to send the signal since each bit has to be sent 3 times.

How does a check digit work?

An extra digit at the end of a datum to check for mistakes in a transmission. This digit can be calculated using an algorithm on the other bits in the datum

How does a checksum work?

The sum of the digits in the datum is sent to be compared with the datum.

What is a drawback of checksums?

Certain errors may cause the same sum to be generated