What Is Binary?
Binary is a base-two number system. It uses only the digits 0 and 1. Each position represents a power of two, rather than the powers of ten used in denary numbers.
Binary Place Values
For an eight-bit value, the place values are 128, 64, 32, 16, 8, 4, 2 and 1. A 1 means the place value is included; a 0 means it is not.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
The included values are 32, 8, 4 and 1. Their total is 45, so 00101101 represents denary 45.
Convert Denary to Binary
Take the value 22. Starting with the largest place value that fits, 16 is included, leaving 6. Eight is not included. Four is included, leaving 2. Two is included and one is not. In eight bits the answer is 00010110.
Why Computers Use Binary
Computer hardware can represent two distinguishable states reliably. We label those states 0 and 1. Larger patterns of bits can then represent numbers, characters, images, instructions and other data.
Common Mistakes
- Writing place values in the wrong order.
- Using powers of ten instead of powers of two.
- Forgetting to include leading zeroes when a fixed bit length is required.
- Adding a place value whose bit is 0.
- Finishing without converting back to check the answer.
Check a Conversion in Reverse
After converting denary 22 to 00010110, add the binary place values back together: 16 + 4 + 2 = 22. This reverse check is quick and catches misplaced bits.
What a Fixed Number of Bits Means
A bit pattern has a fixed number of positions. With four unsigned bits, the smallest value is 0000 and the largest is 1111. The largest value is 8 + 4 + 2 + 1 = 15. Adding another bit creates another place value and increases the available combinations.
This article focuses on unsigned whole numbers. Other representations use bit patterns differently, so students should keep the type of representation clear.
Practice Questions
- Convert
00001101to denary. - Write denary 42 as an eight-bit binary value.
- What is the largest unsigned value that can be represented using six bits?
The answers are 13, 00101010 and 63. For the final question, add 32 + 16 + 8 + 4 + 2 + 1.
Why Binary Supports Other Topics
Secure understanding of place values helps when students study data representation, bit depth, colour depth, character encoding and binary arithmetic. The later topic may look different, but careful alignment and powers of two remain important.
Next, read about computational thinking, explore revision resources, or ask about GCSE tuition.