Place values in base 2 and base 16, converting between the three bases, and units from bits to terabytes.
What you will learn
- Convert between binary, denary and hexadecimal
- Say why hexadecimal is used
- Convert between units of data
- Work out how many bits are needed
Binary place values
Computers store everything as binary (base 2): 0s and 1s, because a circuit is either off or on.
One binary digit is a bit.
Each bit is worth twice the one to its right. The ordinary numbers we count with, using the digits 0 to 9, are denary (base 10).
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
1011 0010 = 128 + 32 + 16 + 2 = 178. To go the other way, take the biggest place value that fits, write 1, subtract, and carry on.
Tap the bits to see the value change.
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- Binary place values
- Hexadecimal
- Units of data
- Try it: Binary to denary
9 practice questions, marked as you go; about 25 minutes in all.
Key terms
Binary, Bit, Denary, Hexadecimal, Binary prefixes, Kibibyte, Mebibyte, Gibibyte, Tebibyte
In this unit: Data representation
Binary, denary and hexadecimal, binary addition and shifts, two's complement, and how characters, images and sound are stored and compressed.
- Binary, denary and hexadecimal
- Binary addition and shifts
- Negative numbers in binary
- Characters and images
- Sound and compression