Number Bases & Conversions Flashcards

All 20 cards in this deck

What is binary?

A number system containing two symbols, 0 and 1, also known as base 2.

Why do computers store and process all data in binary?

They work with electrical signals that are either on or off, which match the two binary digits 1 and 0.

What do computers use binary to represent?

All data and instructions. Text, images and sound must all be converted into binary before a computer can store or process them.

What are the eight place values of an 8-bit binary number?

128, 64, 32, 16, 8, 4, 2, 1.

What is the largest decimal number that can be stored in 8 bits?

255 (11111111).

What are the steps to convert a decimal number to 8-bit binary?
e.g. convert 20

1. Write the place values 128 64 32 16 8 4 2 1.
2. Working from the left, put a 1 where the value fits and subtract it: 16, then 4.
3. Fill the rest with 0s: 00010100.

What are the steps to convert an 8-bit binary number to decimal?
e.g. convert 00001101

1. Write the place values above the bits.
2. Add the place values wherever there is a 1: $8 + 4 + 1$.
3. Answer: 13.

What is hexadecimal?

A base 16 number system using the digits 0–9 and the letters A–F.

What decimal values do the hex digits A and F represent?

A = 10 and F = 15.

What is the largest decimal number that can be written as a 2-digit hexadecimal number?

255, written as FF.

True or false? Hexadecimal is used because it is easier for people to read, remember and type than binary.

True. Two hex digits replace eight binary digits. The computer still stores and processes the value in binary.

What are the steps to convert a decimal number to 2-digit hexadecimal?
e.g. convert 60

1. Divide by 16: $60 \div 16 = 3$ remainder 12.
2. The whole number is the first hex digit: 3.
3. The remainder as a hex digit is the second: 12 = C, giving 3C.

What are the steps to convert a 2-digit hexadecimal number to decimal?
e.g. convert 2A

1. Multiply the first digit by 16: $2 \times 16 = 32$.
2. Find the value of the second digit: A = 10.
3. Add them: $32 + 10 = 42$.

How many binary digits does one hexadecimal digit represent?

4 binary digits, so two hex digits represent one byte.

What are the steps to convert an 8-bit binary number to hexadecimal?
e.g. convert 11011010

1. Split into two groups of 4 bits: 1101 and 1010.
2. Convert each group to decimal: 13 and 10.
3. Write each as a hex digit: DA.

What are the steps to convert a 2-digit hexadecimal number to binary?
e.g. convert 4F

1. Take each hex digit separately.
2. Convert each to 4 bits: 4 = 0100, F = 1111.
3. Join them: 01001111.

True or false? Writing a value in hexadecimal makes it take up less memory and be processed faster than binary.

False. Hexadecimal is only for people to read. The computer still stores and processes the value as exactly the same binary.

What decimal values do the hex digits B, C, D and E represent?

B = 11, C = 12, D = 13 and E = 14. (A = 10 and F = 15.)

What is decimal?

A base 10 number system that uses the ten digits 0–9. It is the number system people use every day.

What is the largest whole number that can be stored in $n$ bits?

$2^n - 1$
e.g. 4 bits can hold up to 15 (1111).