The binary and denary number systems, why computers store data in binary, the units of data capacity, and converting whole numbers between binary and denary.

What this topic is asking

WJEC wants you to know why computers store everything in binary, the units used to measure data capacity, and how to convert whole numbers between binary (base 2) and denary (base 10). This is the foundation of the Data representation and data types content in Unit 1 of WJEC GCSE Computer Science (3500).

Why computers use binary

A single binary digit is called a bit (short for binary digit). Because one bit can only be $0$ or $1$, it can store just two different values; to store more, you group bits together.

Units of data capacity

So $1\,\text{KB} = 1000$ bytes, $1\,\text{MB} = 1000\,\text{KB}$, $1\,\text{GB} = 1000\,\text{MB}$ and $1\,\text{TB} = 1000\,\text{GB}$. The number of different values that $n$ bits can store is $2^n$: one bit stores $2$ values, two bits store $4$, and a full byte of $8$ bits stores $2^8 = 256$ different values, from $0$ to $255$.

Place value in binary

Converting binary to denary

To convert a binary number to denary, write the place values above the bits and add up every place value that has a $1$ beneath it.

Converting denary to binary

The reliable method is to keep subtracting the largest power of $2$ that fits, writing a $1$ in that column and a $0$ in any column you skip. An alternative is repeated division by $2$, writing the remainders and reading them from bottom to top, but the subtraction method is usually quicker for the small numbers in the exam.

Try this

Q1. Convert $11000110$ to denary. [2 marks]

• Cue. $128 + 64 + 4 + 2 = 198$.

Q2. State how many different values can be stored in $4$ bits. [1 mark]

• Cue. $2^4 = 16$ different values.