Binary and Hexadecimal Basics Exam Questions

• C 16 (1)
• The only correct answer is C. The correct answer is 16.
• A is not correct because 4 is the number of bits in the pattern, not the number of states it can represent
• B is not correct because 8 is the number of states a 3-bit pattern can represent
• D is not correct because 32 is the number of states a 5-bit pattern can represent

• A It uses fewer digits than binary to represent the same value (1)
• The only correct answer is A. The correct answer is that hexadecimal uses fewer digits than binary to represent the same value.
• B is not correct because binary can represent the same range of values for a given number of bits
• C is not correct because a computer processes binary data and instructions, so hexadecimal must be converted before it is processed
• D is not correct because hexadecimal uses the digits 0 to 9 and the letters A to F

Award one mark for:

• 16 (1)

Allow 2^4, 2 × 2 × 2 × 2 or any expression that evaluates to 16.

Allow sixteen (in words).

Do not accept 15.

Award one mark for any of the following up to a maximum of two marks:

• Computer components/hardware have two states, on and off (1)
• Digital circuits/switches/transistors have two stable states (1)
• Two states are easy to distinguish/detect reliably (1)
• Fewer errors occur because only two voltage levels need to be recognised (1)
• Binary is simple to implement in hardware because only two states/two voltage levels are needed (1)
• Binary is cheaper to build than a system with more states, as fewer components/levels are needed (1)

Award a maximum of one mark for reasons about reliability/errors, however they are phrased (e.g. 'two states are easy to distinguish' and 'less chance of error' are the same reason).

Do not accept 'it is simple' or 'it is cheap' without a justification.

Do not accept 'computers only understand 1s and 0s' on its own.

Do not accept a restatement of the stem or of the question, e.g. 'computers use binary to store data' or 'because that is how data is stored', with no reason given.

Award one mark for any of the following up to a maximum of two marks:

• Hexadecimal is shorter than binary/uses fewer digits (1)
• It is quicker/easier to read/write (than binary) (1)
• It is easier to remember (than binary) (1)
• Fewer digits mean less chance of error when reading or typing (1)
• It is easy to convert between hexadecimal and binary (1)

Do not accept 'easier'/'better' on its own without saying what is easier/better, e.g. easier to read/write.

For the less chance of error point, accept reading or typing on its own.

Do not award the less chance of error point for a response that only says hexadecimal is shorter/uses fewer digits.

Do not award two marks for the same reason repeated in different words; a second, different reason is needed for the second mark.

Do not accept hexadecimal takes less storage space/uses less memory than binary.

Award up to two marks for a linked description such as:

• The circuits/switches inside a computer can only be in one of two states, on or off (1) so a bit with the values 1 and 0 can represent each of these states (1)
• Electronic components have two states, such as a high or low voltage (1) so only two symbols can be stored reliably (1)
• A binary digit has only two possible values, 0 and 1 (1) so all data (numbers, text, sound, graphics, instructions) can be stored as a pattern of these two values (1)
• The two states are clearly different, e.g. a high voltage and a low voltage (1) so data is less likely to be misread (1)
• Data is stored and processed by components that can only hold two states (1) so all data must be converted into 1s and 0s before it can be processed (1)

Do not accept responses that only state that computers use/understand 0s and 1s, e.g. 'computers only understand binary', or that repeat the question.

For the 'misread' point, accept a description of the clear difference between the two states, such as high/low voltage or on/off. Do not accept a claim that binary is 'more accurate' on its own.

Do not accept reasons about hexadecimal being shorter or easier to read, as these do not explain why binary is used.

Award up to two marks for a linked description such as:

• Each bit has two possible values/states (0 or 1) (1) so the number of codes is 2 × 2 × 2 × 2 = 16 (1)
• The number of bits is used as the power of 2 (1) so for 4 bits the number of codes is 2^4 = 16 (1)
• Each extra bit doubles the number of possible codes (1) so 4 bits give 2 × 2 × 2 × 2 = 16 codes (1)

Do not accept 15 (or 2^4 − 1): this is the largest value a 4-bit pattern can hold, not the number of different codes.

Do not award a response that only states 16 or '2^4 = 16' without a linked description.

Do not award '2 to the power of 4' on its own without a linked description, such as two values per bit or the number of bits used as the power of 2.

Award up to two marks for a linked explanation such as:

• (Computers) are made of electronic components/switches/transistors that have two states, on/off (1) so binary's two values 0 and 1 can represent these states (1)
• Data stored as binary is more resistant to errors (1) because only two voltage levels/states need to be distinguished, so electrical noise/interference is less likely to be misread as a different value (1)
• Circuits that only need to distinguish two states are simpler/cheaper to manufacture (1) because each component only needs to hold one of two stable states (1)

For both marks, the expansion must follow/associate with the statement.

Do not accept 'computers only understand 0s and 1s' as a reason on its own without saying what the two states are or why binary matches them.

Do not accept 'computers are digital' or 'that is how computers work' without expansion.

Do not accept 'binary is easier to read/write' or 'binary is easier to understand' as a reason for using binary.

Do not award the same point twice if it is repeated in different words, e.g. two answers that both say circuits/components are on or off.

Award up to two marks for a linked explanation such as:

• Each bit has two possible values, 0 and 1 (1) so the five bits give 2 × 2 × 2 × 2 × 2/2^5 = 32 different combinations/states (1)
• Because each of the five bits can be either 0 or 1 (1) there are 2^5/2 × 2 × 2 × 2 × 2 = 32 different combinations/states (1)
• Each extra bit doubles the number of combinations/states (1) so five bits give 2^5 = 32 states (1)

For both marks, the expansion must follow/associate with the statement.

Do not award a response that only repeats the 32 states given in the question, such as 'it can represent 32 states' or '2^5 = 32', without a reason about each bit having two possible values.

Do not accept 2 × 5 = 10 as the calculation; the number of states doubles with each extra bit.

Do not accept 31/0 to 31 as the number of states; 31 is the largest value five bits can store, not the number of states.

Award up to two marks for a linked explanation such as:

• Hexadecimal is shorter/has fewer digits than binary (1) because each hexadecimal digit represents 4 bits/a nibble (1)
• Hexadecimal is easier to read/write (1) because there are fewer characters/digits to enter (1)
• Hexadecimal is easier to convert to and from binary (1) because four binary bits map to one hexadecimal digit (1)

For both marks, the expansion must follow/associate with the statement.

Allow the 24-bit colour as the linked reason, e.g. a 24-bit value can be written as only 6 hexadecimal digits (1).

Do not accept 'easier'/'simpler' on its own: naming what is easier, such as easier to read/write, is the first mark, but the second mark needs a linked reason.

Only credit 'fewer digits/characters' once, as the reason for one point; do not award it again as the reason for a second point.

Do not accept that hexadecimal uses less storage space/memory than binary, or that it is more compact to store; the same number of bits is stored.