The ability to carry out binary arithmetic is not required. Knowledge of…

The idea

You do not need to add, subtract, multiply or divide in binary. Instead, you should understand that digital signals are represented by discrete binary levels, usually 0 and 1, and that a short sequence of bits can encode small whole numbers. Learn the binary patterns for the decimal numbers 1 to 10, for example 1 = 0001, 2 = 0010, 3 = 0011, 4 = 0100, 5 = 0101, 6 = 0110, 7 = 0111, 8 = 1000, 9 = 1001 and 10 = 1010 in four-bit form. You should be able to recognise these patterns, relate each bit to a power of two, and explain that more bits allow more levels or values. This supports understanding of analogue-to-digital conversion, sampling and resolution without requiring binary calculation.

What earns the marks

• States that digital signals use discrete levels, commonly two voltage levels labelled 0 and 1, whereas analogue signals vary continuously.
• Recognises the binary representations of the decimal numbers 1 to 10, such as 5 = 0101 and 10 = 1010 in four-bit form.
• Explains that each binary digit corresponds to a power of two, for example the rightmost bit represents 2⁰, the next 2¹, then 2² and 2³.
• Describes how a group of bits can represent a finite set of values, so more bits increase the number of possible levels or values.
• Relates binary representation to digital signals by stating that a sequence of 0s and 1s can encode a number or sample value.
• Distinguishes between recognising binary patterns and performing binary arithmetic, noting that arithmetic is not required by this specification statement.

Common mistakes and how to put them right

• Writing binary numbers with the wrong place values, for example treating 0101 as eleven rather than five.

  Put it right by remembering the place values 8, 4, 2 and 1 from left to right in a four-bit number.

• Confusing the number of bits with the number of possible values.

  Put it right by stating that n bits give 2ⁿ possible patterns, so four bits give 16 patterns.

• Attempting full binary addition or subtraction when only recognition of the numbers 1 to 10 is required.

  Put it right by focusing on reading and interpreting the patterns rather than calculating with them.

• Assuming that binary digits must always be written in groups of four.

  Put it right by noting that four-bit examples are used here for clarity, but the number of bits depends on the system.

Exam tips

• Practise converting the decimal numbers 1 to 10 into binary and back until you can recognise each pattern quickly without calculation.
• When a question shows a digital waveform, identify the high and low levels as 1 and 0 before interpreting the sequence.
• Use the phrase 'discrete levels' for digital signals and 'continuous variation' for analogue signals to make your comparison precise.
• If asked about resolution, link the number of bits to the number of possible values rather than attempting binary arithmetic.