Binary to denary

Binary is the number system computers use. It uses two digits, 0 and 1.

Denary is the number system we use most often. It uses ten digits, 0 to 9.

A binary digit is called a bit. Each bit position has a value. From right to left, the values are 1, 2, 4, 8, 16, 32, 64, and so on.

To convert binary to denary, add the place values for every 1 bit.

Worked example.

Binary number: 1011

The bits stand for 8, 4, 2, 1.

1011 means 8 + 0 + 2 + 1.

So the denary value is 11.

A correct answer should show the place values, then add the values for the 1 bits. A common mistake is to read the bits as if they were ordinary denary digits.

More practice

In these questions, convert each binary number to denary.

Use the place values first. Then add the values where the bit is 1. Check that your final answer is a whole number in base 10.