nce/aqa/questions","basePath":"/gcse/computer-science/aqa/binary-arithmetic/questions","formulaUrl":null,"initialIndex":3,"initialQuestionWindow":[{"id":"194f0c05-29c1-4eea-b171-d4488661c438","revisionId":"c94f8cfe-2192-448f-8e94-b49f5bff69eb","questionNumber":null,"questionType":"LA","specification":"","difficulty":4,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"ffbe68f6-0a41-4a41-bf78-d8049e861e68","label":null,"content":"A microcontroller retrieves three 8-bit register values representing telemetry data:\n\n$$\\begin{array}{r}\n 0\\ 0\\ 1\\ 1\\ 0\\ 1\\ 0\\ 1 \\\\\n 0\\ 1\\ 0\\ 1\\ 1\\ 0\\ 1\\ 0 \\\\\n +\\ 0\\ 0\\ 1\\ 0\\ 0\\ 1\\ 1\\ 1 \\\\\n \\hline\n \\\\\n \\hline\n \\end{array}$$\n\nCalculate the total sum of these three values, presenting your working and final answer as an 8-bit binary number.","markscheme":"- Converts the binary values to decimal as $53$, $90$, and $39$, leading to a sum of $182$, or shows correct column-by-column binary addition with carry bits M1\n- Provides the final correct 8-bit binary string $10110110$ A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"binary_column_addition","label":"Binary column addition","steps":[{"type":"text","order":0,"title":"Read the values","content":"First, group the digits on each row into an 8-bit binary number:\n\n$$00110101,\\qquad 01011010,\\qquad 00100111$$\n\nWork from the rightmost column, because that is the $1$s column. In binary, a total of $2$ in a column is written as $0$ and carries $1$ into the next column."},{"type":"hyper_latex","block":{"nodes":[{"latex":"1+0+1=2\\quad\\Rightarrow\\quad\\text{write 0 and carry 1}"},{"latex":"\\begin{array}{r}11111110\\\\00110101\\\\01011010\\\\+\\,00100111\\\\\\hline\\color{@sky}{10110110}\\end{array}"},{"text":"The completed total is 10110110, which is already 8 bits long. This earns the A1 mark for the correct final 8-bit binary answer."}]},"order":1,"title":"Add the columns","description":"Add from right to left, carrying whenever a column total is 2 or 3. The carry row records the carry into the column underneath it, which earns the M1 mark."}]}],"generatedAt":"2026-07-21T17:41:36.312Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"202897ed-d8db-4d33-a086-5ade8dec99cc","revisionId":"87e11869-41a8-43de-a1f6-270c87ddf28f","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"1e7b1112-5533-4c6f-9ca4-9f1ed5d3c0e0","label":null,"content":"A digital pressure sensor on an autonomous underwater vehicle registers an offset represented by the following 8-bit unsigned binary pattern:\n\n`11011000`\n\nTo scale this measurement, the onboard processor performs a logical right binary shift of 3 on the pattern.\n\nDetermine the resulting 8-bit pattern after this shift.","markscheme":"- Identifies that a logical right shift of 3 moves all bits three positions to the right, discarding the three rightmost bits and padding the leftmost positions with three 0s (or shows an intermediate shift or correctly calculates $216 \\div 8 = 27$) M1\n- States the final 8-bit pattern as `00011011` A1","marks":2,"order":0,"markingRubric":null,"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"21987bee-547d-497c-bea3-549e3d8e4307","revisionId":"371eec40-e3b9-4b50-8fd8-cd59134da794","questionNumber":null,"questionType":"LA","specification":"","difficulty":3,"difficultyBand":"easy","totalMarks":1,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"c2664ea5-fedf-481b-817f-3018d9169aa1","label":null,"content":"Apply a binary shift two places to the right on the bit pattern `11011000`.\n\nGive the result using 8 bits.","markscheme":"- States the correct 8-bit pattern `00110110` B1","marks":1,"order":0,"markingRubric":null,"e

Binary arithmetic

Question 3

Binary arithmetic Questions

Binary arithmetic

Question 3

Binary arithmetic Questions