Bits and binary numbers

Step 1 Warm-up recall

From Module 1: write the three parts of every computational problem.

Your answer

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Step 2 Learning goal

By the end of this lesson you can:

• define bit and binary (Foundation);
• read a binary number using place values (Core);
• state how many values n bits can hold (Core).

Step 3 A familiar example

An ordinary light switch is either off or on. A computer is built from billions of tiny switches like that, so everything it stores must be written with just two symbols.

Step 4 Clear explanation

A bit (binary digit) is a single value that is either 0 or 1. Binary is a way of writing numbers using only those two symbols. We use the same idea in everyday decimal numbers, where each place is worth ten times the place to its right (ones, tens, hundreds). In binary, each place is worth two times the place to its right: 1, 2, 4, 8, 16 and so on.

To read a binary number, add the worth of every place that holds a 1. Here the places holding a 1 are worth 8, 2 and 1, so the number is 11. With n bits there are 2 multiplied by itself n times different patterns, written 2ⁿ. Four bits give 16 patterns, which represent the numbers 0 to 15.

The chart shows why eight bits, the size of a byte, are so common: they give 256 patterns, enough for the numbers 0 to 255. For background on the machine itself, see the entry on the computer.

Step 5 Worked example (4 marks)

Read the binary number 1101.

1. Write the place values from the left: 8, 4, 2, 1. (1 mark)
2. Match the bits: 1, 1, 0, 1. (1 mark)
3. Add the places holding a 1: 8 + 4 + 1. (1 mark)
4. Answer: 13. (1 mark)

Step 6 Learner practice (instant-marked)

Step 7 Recap

• A bit is 0 or 1; binary uses only those two symbols.
• Place values double from the right: 1, 2, 4, 8, 16.
• n bits give 2 to the power n patterns.

Step 8 Exit ticket (ungraded)

Read the binary number 10010 and write it as a decimal number.

Your answer

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Step 9 Go further (Extension)

Read the encyclopedia entry on the computer and note one component that stores data.