- Define and explain Binary Numbers in your own words
- Use key terms such as denary accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
Every photo, song, message and game on your devices is stored as billions of tiny switches, each either on or off. Data representation is the clever set of codes that turns those ones and zeros into everything a computer shows you. Once you can read binary, you can see through the magic.
This lesson focuses on Binary Numbers: count in base 2 and convert between binary and denary.
Count in base 2 and convert between binary and denary.
Key ideas
Place value works in any base
Denary uses columns worth 1, 10, 100 and so on; binary uses columns worth 1, 2, 4, 8, 16 and so on, doubling each time. To convert binary to denary, add up the column values where there is a 1 — so 1011 means 8 + 2 + 1 = 11.
Everything is binary underneath
Text, images, sound and video are all stored as patterns of bits — the computer just interprets the patterns differently. The binary pattern 01000001 means the letter 'A' in text, but the same pattern could mean the number 65 or a dark pixel in an image. Meaning comes from context, not from the bits themselves.
Key term — denary: The ordinary base-10 number system we use every day, with the digits 0 to 9. Also called decimal.
Convert the binary number 1101 to denary.
13 — that is 8 + 4 + 1.
Answer: 13 — that is 8 + 4 + 1.
- Reading binary left to right as if the leftmost digit is worth 1 Correction: the rightmost column is always worth 1 — write the place values above the digits before adding.
- Thinking 8 bits can store the number 999 Correction: 8 bits hold 0 to 255 only; larger numbers need more bits — check 2 to the power of n first.
Practice
10100 — that is 16 + 4.
65 — and the same bits could be a colour value or part of an image, because meaning comes from how the program interprets the bits.
A higher rate takes more samples every second, so more numbers must be stored — better quality costs more bits.
True — each extra bit doubles the combinations, since every existing pattern can end in either 0 or 1.
Quick check
Which of these best defines "denary"?
How many different values can 4 bits represent?
- Binary Numbers: count in base 2 and convert between binary and denary.
- Place value works in any base: Denary uses columns worth 1, 10, 100 and so on; binary uses columns worth 1, 2, 4, 8, 16 and so on, doubling each time.
- bit: A single binary digit — a 0 or a 1.
- Watch out for: reading binary left to right as if the leftmost digit is worth 1