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base.","correct":false,"explanation":"Division moves towards smaller place values, which happens when moving right. Moving one column left increases the value by multiplying the previous place value by the base."},{"text":"It is unchanged.","correct":false,"explanation":"Every column has a different place value, so it cannot remain unchanged. Moving left increases the place value by a factor equal to the number base."},{"text":"It is multiplied by the column number.","correct":false,"explanation":"Place values depend on powers of the base, not on simply counting the column. Each move left multiplies the value by the base itself."}]},{"id":"581f9e59-e2fb-42f4-a85b-752adeb157a9","cardType":"cloze","points":null,"front":"Decimal is base [ ]; binary is base [ ].","back":"Decimal is base 10; binary is base 2.","mcqOptions":[{"text":"Decimal is base 10; binary is base 2.","correct":true,"explanation":"Decimal uses ten symbols, 0 to 9, so it is base 10. Binary uses only 0 and 1, so it is base 2."},{"text":"Decimal is base 2; binary is base 10.","correct":false,"explanation":"This reverses the two bases. Decimal is based on ten digits, whereas binary is based on two possible digits, 0 and 1."},{"text":"Decimal is base 16; binary is base 2.","correct":false,"explanation":"Binary is correctly identified as base 2, but hexadecimal, not decimal, is base 16. Decimal uses ten digits and is therefore base 10."},{"text":"Decimal is base 10; binary is base 8.","correct":false,"explanation":"Decimal is correctly identified as base 10, but base 8 is octal. Binary has only two digits, so its base is 2."}]},{"id":"374b6ecc-4681-494d-a34b-a9fa1a2c2833","cardType":"cloze","points":null,"front":"The written digits 10 mean [ ] in binary and [ ] in hexadecimal.","back":"The written digits 10 mean two in binary and sixteen in hexadecimal.","mcqOptions":[{"text":"The written digits 10 mean two in binary and sixteen in hexadecimal.","correct":true,"explanation":"In binary, the 1 is in the twos column, giving two. In hexadecimal, the digits 10 represent one sixteen, giving sixteen."},{"text":"The written digits 10 mean ten in binary and sixteen in hexadecimal.","correct":false,"explanation":"The hexadecimal interpretation is right, but binary place values are powers of two. Binary 10 means one two and zero ones, which equals two."},{"text":"The written digits 10 mean two in binary and ten in hexadecimal.","correct":false,"explanation":"The binary interpretation is right, but hexadecimal uses sixteen as its base. Hexadecimal 10 therefore means one sixteen, not ten."},{"text":"The written digits 10 mean ten in binary and ten in hexadecimal.","correct":false,"explanation":"This treats the written digits as decimal in both bases. Their value depends on the base: binary 10 is two, while hexadecimal 10 is sixteen."}]},{"id":"e6b8db1c-42fa-4439-b141-25cd19d93c1b","cardType":"basic","points":2,"front":"Why do computers use binary?","back":"Two-state electronic circuits reliably represent 0 and 1.","mcqOptions":[{"text":"Two-state electronic circuits reliably represent 0 and 1.","correct":true,"explanation":"Electronic circuits can reliably use two distinct states, such as low and high voltage. These states map naturally to the binary values 0 and 1."},{"text":"Two-state electronic circuits reliably represent 0 and 2.","correct":false,"explanation":"Two-state circuits provide two possible states, which are represented as 0 and 1. Using 0 and 2 would not match binary’s digit system."},{"text":"Ten-state electronic circuits reliably represent 0 and 1.","correct":false,"explanation":"Binary is used because circuits can reliably distinguish two states, not ten. Ten possible states would correspond more closely to decimal representation."},{"text":"Continuous electronic circuits reliably represent 0 and 1.","correct":false,"explanation":"Continuous signals can be affected by noise and small changes. Digital circuits use two distinct states because they are easier to distinguish reliably as 0 and 1."}]},{"id":"af3fdd61-d253-4f78-9fd9-da0bbf33c3e1","cardType":"cloze","points":null,"front":"A [ ] is a single 0 or 1; a [ ] is a sequence of bits.","back":"A bit is a single 0 or 1; a bit pattern is a sequence of bits.","mcqOptions":[{"text":"A bit is a single 0 or 1; a bit pattern is a sequence of bits.","correct":true,"explanation":"A bit is the smallest binary unit and can hold either 0 or 1. A bit pattern is an ordered sequence containing multiple bits."},{"text":"A byte is a single 0 or 1; a byte pattern is a sequence of bits.","correct":false,"explanation":"A byte is normally a group of eight bits, not one binary digit. A single 0 or 1 is a bit, and a sequence of bits is a bit pattern."},{"text":"A digit is a single 0 or 1; a bit pattern is a sequence of bits.","correct":false,"explanation":"Although 0 and 1 are digits, the specific computer science term for one binary digit is bit. A sequence of bits is correctly called a bit pattern."},{"text":"A bit is a single 0 or 1; a byte is a sequence of bits.","correct":false,"explanation":"The first term is correct, but a byte has a specific size of eight bits. A sequence of bits in general is called a bit pattern."}]},{"id":"9d3a047f-e599-457b-81de-679d0147c1dc","cardType":"basic","points":1,"front":"In an 8-bit binary number, what does the rightmost bit represent?","back":"The ones column.","mcqOptions":[{"text":"The ones column.","correct":true,"explanation":"The rightmost binary position is $2^0$, which equals one. Therefore, it is the ones column, just as the rightmost decimal position is also the ones column."},{"text":"The twos column.","correct":false,"explanation":"The twos column is immediately to the left of the rightmost position. The rightmost bit has place value $2^0$, or one, so it is the ones column."},{"text":"The eights column.","correct":false,"explanation":"The eights column is the fourth position from the right in an 8-bit number. The rightmost position is $2^0$, giving the ones column."},{"text":"The 128s column.","correct":false,"explanation":"The 128s column is the leftmost position in an 8-bit binary number. Place values decrease towards the right, ending with the ones column."}]},{"id":"7bae2d96-4f58-4e27-a70f-26205fc48c3f","cardType":"basic","points":2,"front":"What are the 8-bit binary place values from left to right?","back":"128, 64, 32, 16, 8, 4, 2, 1.","mcqOptions":[{"text":"128, 64, 32, 16, 8, 4, 2, 1.","correct":true,"explanation":"An 8-bit binary number uses powers of two from $2^7$ down to $2^0$. These give 128, 64, 32, 16, 8, 4, 2 and 1."},{"text":"256, 128, 64, 32, 16, 8, 4, 2.","correct":false,"explanation":"This sequence starts at $2^8$ and ends at $2^1$, as if the eight positions had been shifted one power left. An 8-bit number starts at $2^7$ and ends at $2^0$."},{"text":"64, 32, 16, 8, 4, 2, 1, 0.","correct":false,"explanation":"The powers of two have been started one place too low and incorrectly ended with zero. The final place value is one, and the leftmost value is 128."},{"text":"128, 96, 64, 48, 32, 16, 8, 4.","correct":false,"explanation":"Place values double or halve between adjacent columns; they do not decrease by a fixed or mixed amount. The correct sequence consists entirely of descending powers of two."}]},{"id":"f54dcd4e-9fef-40a8-98bb-d48aad005ec9","cardType":"basic","points":1,"front":"If 1011 0010 is a positive integer, what decimal value does it represent?","back":"178.","mcqOptions":[{"text":"178.","correct":true,"explanation":"The 1s represent 128 and 32, 16, and 2 are also present: $128 + 32 + 16 + 2 = 178$. The zero bits contribute nothing."},{"text":"162.","correct":false,"explanation":"This omits the value of the fourth bit from the left, which is 16. Adding every set bit gives $128 + 32 + 16 + 2 = 178$."},{"text":"179.","correct":false,"explanation":"This is the result of adding an extra one, usually by treating the final zero as a set bit. The set bits total $128 + 32 + 16 + 2 = 178$."},{"text":"194.","correct":false,"explanation":"This incorrectly counts the second bit as 64 even though it is zero, while missing the set 16 bit. The correct total is $128 + 32 + 16 + 2 = 178$."}]},{"id":"c9abd4a6-e0b1-4781-90c8-b99795a622bf","cardType":"basic","points":1,"front":"A computer represents all data in what form?","back":"As bit patterns.","mcqOptions":[{"text":"As bit patterns.","correct":true,"explanation":"Computers represent data as sequences of binary digits, or bits. Different bit patterns can represent numbers, text, images, sound or other data depending on how they are interpreted."},{"text":"As decimal values.","correct":false,"explanation":"Decimal values are one possible interpretation, but computers store data electronically as binary bit patterns. The correct answer is bit patterns because every data type is encoded using sequences of bits."},{"text":"As hexadecimal symbols.","correct":false,"explanation":"Hexadecimal is a convenient shorthand for displaying binary, not the fundamental representation used by a computer. The correct answer is bit patterns, made from binary digits 0 and 1."},{"text":"As ASCII characters.","correct":false,"explanation":"ASCII characters represent text, but computers also store numbers, images, sound and instructions. The general representation is bit patterns, whose meaning depends on the data type and context."}]},{"id":"6ef18702-a277-41ef-aaf7-23987a52c8c7","cardType":"basic","points":1,"front":"Besides data, what else does a computer represent in binary?","back":"Instructions.","mcqOptions":[{"text":"Instructions.","correct":true,"explanation":"Instructions are also represented in binary so that the processor can fetch, decode and execute them. Their bit patterns specify operations and the data or addresses involved."},{"text":"File names.","correct":false,"explanation":"File names are data stored using character encodings, rather than the separate category asked for here. The correct answer is instructions, which tell the processor what operations to perform."},{"text":"Screen pixels.","correct":false,"explanation":"Screen pixels are an example of data, such as image or display data. Besides data, computers represent instructions in binary so the processor can execute programs."},{"text":"Network cables.","correct":false,"explanation":"Network cables carry signals but are not something a computer represents as binary. The additional thing represented in binary is instructions, which control processor operations."}]},{"id":"4eaab7ea-6a4f-4a4c-8345-949c456c5b7d","cardType":"basic","points":2,"front":"What gives a bit pattern its meaning?","back":"Context, such as the program, file format, character set or processor.","mcqOptions":[{"text":"Context, such as the program, file format, character set or processor.","correct":true,"explanation":"The same bit pattern can mean different things in different situations. The program, file format, character set or processor provides the context needed to interpret it correctly."},{"text":"Length, such as the number of bits, bytes, characters or instructions.","correct":false,"explanation":"Length tells you how much storage a pattern occupies, but not necessarily what it means. The correct answer is context, including the program, file format, character set or processor."},{"text":"Colour, such as the brightness, hue, saturation or contrast.","correct":false,"explanation":"Colour can be encoded by bit patterns for images, but it does not determine the meaning of every pattern. Context, such as a file format or character set, does."},{"text":"Location, such as the memory address, sector, register or cache.","correct":false,"explanation":"Location identifies where a pattern is stored, not how it should be interpreted. The correct answer is context, supplied by things such as the program, file format or processor."}]},{"id":"89640bba-fff5-4d63-b320-af7ccc8d5a0a","cardType":"cloze","points":null,"front":"0100 0001 represents [ ] as a positive integer, and commonly [ ] in ASCII text.","back":"0100 0001 represents 65 as a positive integer, and commonly A in ASCII text.","mcqOptions":[{"text":"0100 0001 represents 65 as a positive integer, and commonly A in ASCII text.","correct":true,"explanation":"The binary number 0100 0001 equals 64 + 1 = 65. ASCII assigns decimal value 65 to the uppercase letter A."},{"text":"0100 0001 represents 64 as a positive integer, and commonly A in ASCII text.","correct":false,"explanation":"The leading 1 in the final position contributes one, so the value is 65 rather than 64. ASCII value 65 represents uppercase A."},{"text":"0100 0001 represents 65 as a positive integer, and commonly B in ASCII text.","correct":false,"explanation":"The numerical conversion is correct, but ASCII value 65 corresponds to uppercase A. Uppercase B is the next value, 66, so this confuses adjacent character codes."},{"text":"0100 0001 represents 66 as a positive integer, and commonly B in ASCII text.","correct":false,"explanation":"Adding the place values gives 64 + 1 = 65, not 66. Although B is a plausible adjacent character, ASCII assigns it value 66 rather than 65."}]},{"id":"91cdf80b-142d-4c3c-aef3-51a2bf1269c1","cardType":"cloze","points":null,"front":"Hexadecimal is base [ ] and uses 0 to 9 plus [ ].","back":"Hexadecimal is base 16 and uses 0 to 9 plus A to F.","mcqOptions":[{"text":"Hexadecimal is base 16 and uses 0 to 9 plus A to F.","correct":true,"explanation":"Hexadecimal has sixteen digit values, 0 to 9 followed by A, B, C, D, E and F, representing values 10 to 15."},{"text":"Hexadecimal is base 8 and uses 0 to 9 plus A to F.","correct":false,"explanation":"Base 8, or octal, has only eight digit values and cannot use 0 to 9. Hexadecimal is base 16 and uses 0 to 9 plus A to F."},{"text":"Hexadecimal is base 16 and uses 0 to 9 plus A to E.","correct":false,"explanation":"Stopping at E provides only fifteen symbols, omitting the value 15. Hexadecimal requires A to F after 0 to 9, giving sixteen symbols in total."},{"text":"Hexadecimal is base 10 and uses 0 to 9 plus A to F.","correct":false,"explanation":"Base 10 uses only the digits 0 to 9, so adding A to F makes the description inconsistent. Hexadecimal is base 16 with six additional symbols."}]},{"id":"f3529585-a735-4bfe-9954-355d97cc9910","cardType":"cloze","points":null,"front":"In hexadecimal, A represents [ ] and B represents [ ].","back":"In hexadecimal, A represents 10 and B represents 11.","mcqOptions":[{"text":"In hexadecimal, A represents 10 and B represents 11.","correct":true,"explanation":"Hexadecimal continues counting after 9: A has value 10 and B has value 11. These symbols represent the first two additional digit values in base 16."},{"text":"In hexadecimal, A represents 9 and B represents 10.","correct":false,"explanation":"This shifts the hexadecimal letter values down by one and treats A as if it followed 8. Since 0 to 9 already occupy ten values, A is 10 and B is 11."},{"text":"In hexadecimal, A represents 10 and B represents 12.","correct":false,"explanation":"A is correctly identified as 10, but hexadecimal counts consecutively, so B must be 11. The value 12 belongs to C, not B."},{"text":"In hexadecimal, A represents 11 and B represents 12.","correct":false,"explanation":"Both values are one too high because the counting after 9 has been started at the wrong point. A represents 10 and B represents 11 in hexadecimal."}]},{"id":"66c5a42d-60e3-40ba-9e73-9cd950eb18bc","cardType":"cloze","points":null,"front":"In hexadecimal, C represents [ ] and D represents [ ].","back":"In hexadecimal, C represents 12 and D represents 13.","mcqOptions":[{"text":"In hexadecimal, C represents 12 and D represents 13.","correct":true,"explanation":"After A = 10 and B = 11, hexadecimal continues with C = 12 and D = 13. Each letter represents the next consecutive digit value."},{"text":"In hexadecimal, C represents 11 and D represents 12.","correct":false,"explanation":"These values shift the sequence down by one, effectively treating B as 10. Since A is 10 and B is 11, C is 12 and D is 13."},{"text":"In hexadecimal, C represents 12 and D represents 14.","correct":false,"explanation":"C is correctly 12, but hexadecimal digits increase by one at each step. D therefore represents 13; 14 is the value of E."},{"text":"In hexadecimal, C represents 13 and D represents 14.","correct":false,"explanation":"Both values are one too high because the letter sequence has been advanced too far. The correct values are C = 12 and D = 13."}]},{"id":"a3870230-7087-4511-8643-d2b060b25b17","cardType":"cloze","points":null,"front":"In hexadecimal, E represents [ ] and F represents [ ].","back":"In hexadecimal, E represents 14 and F represents 15.","mcqOptions":[{"text":"In hexadecimal, E represents 14 and F represents 15.","correct":true,"explanation":"The hexadecimal sequence ends with E = 14 and F = 15 after A = 10, B = 11, C = 12 and D = 13."},{"text":"In hexadecimal, E represents 13 and F represents 14.","correct":false,"explanation":"These values are one too low, as though the sequence began with A = 9. The six hexadecimal letters represent 10 through 15, so E = 14 and F = 15."},{"text":"In hexadecimal, E represents 14 and F represents 16.","correct":false,"explanation":"E is 14, but F is the final single hexadecimal digit and therefore represents 15. The value 16 is the base itself, not a hexadecimal digit symbol."},{"text":"In hexadecimal, E represents 15 and F represents 16.","correct":false,"explanation":"Both values are one too high because the sequence has been shifted after D. E represents 14 and F represents 15; 16 requires two hexadecimal digits, such as 10."}]},{"id":"b5b887c9-8e55-4ef0-be6c-c22070220ac8","cardType":"basic","points":1,"front":"What group of bits does one hexadecimal digit represent?","back":"One nibble - 4 bits.","mcqOptions":[{"text":"One nibble - 4 bits.","correct":true,"explanation":"A hexadecimal digit has 16 possible values, matching the 16 patterns produced by 4 binary bits. Therefore, one hexadecimal digit represents exactly one nibble."},{"text":"One byte - 8 bits.","correct":false,"explanation":"A byte contains 8 bits, which can be represented by two hexadecimal digits. A single hexadecimal digit represents only one nibble, containing 4 bits."},{"text":"One bit - 1 bit.","correct":false,"explanation":"A bit has only two possible values, whereas one hexadecimal digit has 16 possible values. Four bits are needed to represent all hexadecimal values from 0 to F."},{"text":"One word - 16 bits.","correct":false,"explanation":"A word is a processor-dependent group of bits and is not fixed at 16 bits. Hexadecimal digits consistently represent four bits, known as a nibble."}]},{"id":"5020f2a9-5210-42be-b186-74da6221aed6","cardType":"basic","points":2,"front":"Why can one hex digit represent one nibble exactly?","back":"$16 = 2^4$, so 4 bits make 16 patterns.","mcqOptions":[{"text":"$16 = 2^4$, so 4 bits make 16 patterns.","correct":true,"explanation":"Each bit has two possible states, so four bits produce $2^4 = 16$ combinations. Hexadecimal has 16 symbols, from 0 to F, giving an exact match."},{"text":"$16 = 2^8$, so 8 bits make 16 patterns.","correct":false,"explanation":"The exponent is too large: $2^8$ equals 256, not 16. Four bits produce the 16 patterns needed for one hexadecimal digit, while eight bits form a byte."},{"text":"$8 = 2^3$, so 3 bits make 8 patterns.","correct":false,"explanation":"This calculation is true for three bits and eight patterns, but hexadecimal requires 16 values. Four bits are needed because $2^4 = 16$."},{"text":"$16 = 2^5$, so 5 bits make 16 patterns.","correct":false,"explanation":"The exponent is off by one: $2^5$ equals 32, not 16. Four binary positions are sufficient because they create exactly 16 distinct patterns."}]},{"id":"9aaec8b4-93a9-4781-828f-2e50a9dbb2f1","cardType":"basic","points":2,"front":"Why should an 8-bit binary pattern become exactly 2 hex digits?","back":"Each hex digit represents 4 bits.","mcqOptions":[{"text":"Each hex digit represents 4 bits.","correct":true,"explanation":"An 8-bit pattern can be split into two groups of four bits. Since each group maps to one hexadecimal digit, the result always contains exactly two hex digits."},{"text":"Each hex digit represents 8 bits.","correct":false,"explanation":"Eight bits make a full byte and require two hexadecimal digits. One hexadecimal digit represents only four bits, so an 8-bit pattern becomes two digits."},{"text":"Each hex digit represents 2 bits.","correct":false,"explanation":"Two bits provide only four possible patterns, which is insufficient for hexadecimal’s 16 values. Four bits are required for each hexadecimal digit."},{"text":"Each hex digit represents 16 bits.","correct":false,"explanation":"Sixteen bits form two bytes and would require four hexadecimal digits. The hexadecimal system groups binary into four-bit sections, not sixteen-bit sections."}]},{"id":"3c21990e-6d5b-41ee-9fc2-5ce2c794c0cd","cardType":"basic","points":1,"front":"Write 1011 0010 in hexadecimal.","back":"B2.","mcqOptions":[{"text":"B2.","correct":true,"explanation":"Split the binary into 1011 and 0010. These four-bit groups have hexadecimal values B and 2, so the complete representation is B2."},{"text":"A2.","correct":false,"explanation":"The second group converts to 2 correctly, but 1011 is 11 in decimal, which maps to B. A represents 1010, so the correct result is B2."},{"text":"B1.","correct":false,"explanation":"The first group converts to B correctly, but 0010 equals 2, not 1. The final hexadecimal digit should therefore be 2, giving B2."},{"text":"D2.","correct":false,"explanation":"The second group is correctly converted to 2, but 1011 is B rather than D. D represents 1101, so the correct conversion is B2."}]},{"id":"c4e1886a-fec0-4603-aa79-ec7909515b69","cardType":"basic","points":3,"front":"Why is hexadecimal useful for humans?","back":"

Shorter than binary.
Easier to read, copy and debug.
Maps neatly to 4-bit groups.

","mcqOptions":[{"text":"

Shorter than binary.
Easier to read, copy and debug.
Maps neatly to 4-bit groups.

","correct":true,"explanation":"Hexadecimal replaces every four binary bits with one symbol, making values more compact and readable. This direct grouping also helps people copy and debug binary data."},{"text":"

Longer than binary.
Harder to read, copy and debug.
Maps neatly to 4-bit groups.

","correct":false,"explanation":"The grouping advantage is correct, but hexadecimal is shorter and generally easier for humans than long binary strings. Its compact notation reduces reading and copying errors."},{"text":"

Shorter than binary.
Easier to read, copy and debug.
Maps neatly to 8-bit groups.

","correct":false,"explanation":"Hexadecimal is compact and readable, but each digit corresponds to four bits, not eight. An 8-bit byte is represented by two hexadecimal digits."},{"text":"

Shorter than binary.
Harder to read, copy and debug.
Maps neatly to 2-bit groups.

","correct":false,"explanation":"Hexadecimal is designed to make binary easier for humans, and each digit maps to four bits. Two-bit groups provide only four values, not all 16 hexadecimal symbols."}]},{"id":"c64db035-6270-4241-8daf-9b8a1a164505","cardType":"basic","points":1,"front":"When binary is displayed as hexadecimal, what does the computer still store?","back":"The computer still stores bits.","mcqOptions":[{"text":"The computer still stores bits.","correct":true,"explanation":"Hexadecimal is only a human-friendly way to display binary data. Internally, computer memory and processing use bits represented by the two states 0 and 1."},{"text":"The computer still stores bytes.","correct":false,"explanation":"A byte is a group of eight bits, not an alternative storage form replacing bits. Hexadecimal display changes notation, while the underlying data remains bits."},{"text":"The computer still stores hexadecimal digits.","correct":false,"explanation":"Hexadecimal digits are a display and representation system for humans. Computers store the corresponding binary states as bits, rather than storing hexadecimal symbols themselves."},{"text":"The computer still stores decimal digits.","correct":false,"explanation":"Decimal digits are another way to write values for people, not the fundamental electronic representation. The computer stores binary states as bits regardless of how values are displayed."}]}]}],"examCountdown":{"examDate":"2027-05-10","paperLabel":"Paper 1"},"heading":"Number bases","title":"Number bases Flashcards","topbar":{"backHref":"/gcse/computer-science/aqa/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"098c4c35-bf49-5ba5-920f-00fc5560baf3","walled":"$L38"}],"$L39","$L3a"]