Cross-Curricular Mixed Question Practice | 跨学科综合题型训练

📚 Cross-Curricular Mixed Question Practice | 跨学科综合题型训练

In Year 7 OCR Computer Science, questions often link computing concepts with mathematics, science, geography and other subjects. This collection of cross-curricular mixed questions will help you practise thinking like a computer scientist while consolidating knowledge from across the curriculum. Work through each problem carefully and check the solutions provided.

在七年级 OCR 计算机科学中，考题经常将计算概念与数学、科学、地理等学科联系起来。这套跨学科综合题型训练将帮助你练习像计算机科学家一样思考，同时巩固跨课程的知识。请仔细完成每道题目并核对给出的解答。

1. Binary and Mathematics | 二进制与数学

Question 1: An 8-bit computer needs to add the numbers 19 and 14. Convert each to binary, then perform binary addition. Show all carries and the final 8-bit result. Verify your answer by converting the binary sum back to denary.

问题1：一台8位计算机需要把19和14相加。先将两个数转换为二进制，然后执行二进制加法。展示所有的进位和最终的8位结果。将二进制和转回十进制来验证答案。

Solution – Step 1 (Conversion): 19 in denary is 16 + 2 + 1. In 8-bit binary, this is 00010011. 14 in denary is 8 + 4 + 2, which gives 00001110.

解答 – 步骤1（转换）：十进制19等于16+2+1。用8位二进制表示为00010011。十进制14等于8+4+2，二进制为00001110。

Step 2 (Addition): Write the numbers aligned, add from rightmost bit: 1+0=1, 1+1=0 carry 1, 0+1+carry=0 carry 1, 0+1+carry=0 carry 1, 0+0+carry=1, 0+0=0, 0+0=0, 0+0=0. The result is 00100001 with a final carry beyond 8 bits (ignored in 8-bit representation).

步骤2（加法）：将数位对齐，从最右位加起：1+0=1, 1+1=0进位1, 0+1+进位=0进位1, 0+1+进位=0进位1, 0+0+进位=1, 0+0=0, 0+0=0, 0+0=0。结果是00100001，最高位产生一个超出8位的进位（在8位表示中被忽略）。

Step 3 (Check): 00100001 binary = 2⁵ + 2⁰ = 32 + 1 = 33 denary. 19 + 14 = 33, so the addition is correct.

步骤3（验证）：二进制00100001 = 2⁵ + 2⁰ = 32 + 1 = 33（十进制）。19 + 14 = 33，因此加法正确。

Question 2: A programmer uses the binary number 1100100 to store the width of an image in pixels. Find the denary value of this number. The image is square, so the total pixel count is the width squared. Square the denary value and convert the result back to binary.

问题2：某程序员用二进制数1100100存储图像的宽度（以像素为单位）。求出这个数的十进制值。该图像是正方形的，因此像素总数等于宽度的平方。计算平方后的十进制值，再将结果转回二进制。

Solution: 1100100₂ = 64 + 32 + 4 = 100 denary. The total pixels = 100² = 10,000. To convert 10,000 to binary: 10,000 = 8192 (2¹³) + 1024 (2¹⁰) + 512 (2⁹) + 256 (2⁸) + 16 (2⁴). So the binary representation is 10011100010000.

解答：二进制1100100₂ = 64 + 32 + 4 = 100（十进制）。总像素数 = 100² = 10,000。将10,000转为二进制：10,000 = 8192 (2¹³) + 1024 (2¹⁰) + 512 (2⁹) + 256 (2⁸) + 16 (2⁴)。因此二进制表示为10011100010000。

2. Logic and Boolean Algebra | 逻辑与布尔代数

Question 1: An alarm system has a door sensor D and a window sensor W. The alarm should sound if either D OR W is triggered. However, a master switch M must be ON for the system to work. Write a Boolean expression for the alarm output Q. Draw a truth table showing all combinations of D, W, M.

问题1：某报警系统装有门磁传感器D和窗磁传感器W。当D或W任一被触发时报警器应响起，但总开关M必须处于开启状态系统才能工作。写出报警输出Q的布尔表达式，并画出表示D、W、M所有组合

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