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bits."},{"id":"a12f7808-692f-40f2-80a4-5c83a99725ac","cardType":"basic","points":1,"front":"What is the binary carry rule for $1 + 1 + carry 1$?","back":"$$11_2$ (write 1 and carry 1)."},{"id":"b3da6f79-372b-4e1d-a5e8-d50ab0e3c4f3","cardType":"basic","points":1,"front":"What is the standard technique for performing binary subtraction?","back":"Add the two's complement of the number being subtracted."},{"id":"b69cd57b-4df2-4610-ac1a-ed848816449e","cardType":"cloze","points":null,"front":"To find the two's complement of a binary number, [ ] then add 1.","back":"To find the two's complement of a binary number, invert the bits then add 1."},{"id":"7d9ce601-6040-4c60-a6bb-f45767aeda0f","cardType":"cloze","points":null,"front":"To find the two's complement of a binary number, invert the bits then [ ].","back":"To find the two's complement of a binary number, invert the bits then add 1."},{"id":"27c196fb-f855-45ad-875c-6ca5a78c4742","cardType":"basic","points":2,"front":"How does the leftmost bit differ between sign-and-magnitude and two's complement?","back":"

Sign-and-magnitude: a sign marker only
Two's complement: a negative place value

"},{"id":"19ae48eb-d7fc-416e-9124-fdd0f921f3db","cardType":"basic","points":2,"front":"What do the mantissa and exponent represent in floating point?","back":"

Mantissa: the significant digits
Exponent: the position of the binary point

"},{"id":"8290ba7e-be59-43f4-bbd4-556e1d996023","cardType":"basic","points":1,"front":"How does increasing the number of exponent bits affect the representation?","back":"Increases the range of values that can be stored."},{"id":"6a889c66-cae6-4c20-9581-08f8df1f130c","cardType":"basic","points":1,"front":"How does increasing the number of mantissa bits affect the representation?","back":"Increases the precision of the stored values."},{"id":"7980a29f-4d20-4413-ad53-cbfd06ecd47c","cardType":"cloze","points":null,"front":"A normalised positive mantissa begins with the bits [ ].","back":"A normalised positive mantissa begins with the bits 0.1."},{"id":"6ff6fd8b-5461-4612-bd73-3999c973519c","cardType":"cloze","points":null,"front":"A normalised negative mantissa begins with the bits [ ].","back":"A normalised negative mantissa begins with the bits 1.0."},{"id":"f0c496c6-4186-406b-ae4f-f56ffceaa9fa","cardType":"basic","points":1,"front":"Identify the OCR symbols for AND, OR, and XOR.","back":"

AND: $∧$
OR: $∨$
XOR: $⊻$

"},{"id":"52dca29b-da02-4cf8-be19-a0ac7c74d3e6","cardType":"basic","points":1,"front":"State De Morgan’s Law for the expression $¬(A ∧ B)$.","back":"$$¬A ∨ ¬B$"},{"id":"aad227ff-0edc-4208-b5c2-56e3d2f11289","cardType":"basic","points":1,"front":"Apply the Distribution Law to $A ∧ (B ∨ C)$.","back":"$$(A ∧ B) ∨ (A ∧ C)$"},{"id":"b4bba1d0-94a9-427a-ac03-bd2285061801","cardType":"basic","points":1,"front":"State the Double Negation law.","back":"$$¬¬A ≡ A$"},{"id":"f41c1648-60f4-4e1f-b3df-70b5419481f0","cardType":"basic","points":2,"front":"What are the rules for valid Karnaugh map groups?","back":"

Rectangles of size powers of 2 ($1, 2, 4, 8...$)
Groups can wrap around edges

"},{"id":"5c01e687-c2b6-49cd-9b52-01118d8b2f6a","cardType":"basic","points":1,"front":"What does Big-O notation measure?","back":"The growth rate of resource use (time/space) as input size $n$ increases."},{"id":"f56fca52-64e4-4010-a6ad-28a71ee71d34","cardType":"cloze","points":null,"front":"Big-O notation simplifies comparisons by ignoring [ ] and smaller terms.","back":"Big-O notation simplifies comparisons by ignoring constants and smaller terms."},{"id":"374df412-1063-4f86-b0cb-d1866496dd6b","cardType":"cloze","points":null,"front":"Big-O notation simplifies comparisons by ignoring constants and [ ].","back":"Big-O notation simplifies comparisons by ignoring constants and smaller terms."},{"id":"a281f2be-d98a-4bc0-8807-3b15d1455416","cardType":"basic","points":1,"front":"What is the typical time complexity of an algorithm with one loop from $0$ to $n-1$?","back":"$$O(n)$ (linear time)."},{"id":"be7060a5-ac56-443f-8d60-194b3302a41b","cardType":"basic","points":1,"front":"What is the time complexity of two nested loops, both iterating $n$ times?","back":"$$O(n^2)$ (polynomial time)."},{"id":"1d339bbc-5e7b-4eb5-9461-3d2eeeef5e65","cardType":"basic","points":2,"front":"Under what conditions is binary search $O(\\log n)$?","back":"

The data is sorted
The middle item can be accessed efficiently

"}]}],"examCountdown":{"examDate":"2027-06-07","paperLabel":"Paper 1"},"heading":"Mathematical skills","title":"Mathematical skills Flashcards","topbar":{"backHref":"/a-level/computer-science/ocr/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"a0f7c825-892f-5923-b584-f64707b2ca74","walled":"$L38"}],"$L39","$L3a"]