Calculating bit values
Alright, I want to work through some calculations: starting with 436 - 256, which equals 180. Then, subtracting 128 gives me 52. I notice 64 doesn’t work, leading me to zero, and moving down to 32 gives me 20. Then, 16 reduces to 4, while 8 drops out, and so does 4, 2, and 1. I'm questioning those bits now — is it 110110100?Calculating number conversions
I'm checking number systems here, starting with binary to decimal conversions. I calculated the decimal as 436 and then went to octal, transforming 110110100 in groups to get 664. For hexadecimal, 0001 1011 0100 turned into 1B4. I'm also verifying some binary numbers like 71 and confirming their octal and hex values.
I need to think about how to show any division algorithms or the calculations in the context of multiplication and division examples that are missing from the task.Addressing task ambiguity
It seems the assignment only includes two operations, even though the heading suggests a broader scope. The user might expect solutions for what's visible, which I can provide. I don’t think I need to ask for clarification just yet, as the image only shows two subitems.
It might be worth adding a note about the missing multiplication and division examples at the end. I can suggest the user send any additional examples if they exist.Considering task examples
I'm thinking for tasks 1-2, it might not be necessary to always show examples, but including base powers principles could be helpful. I could also give a decimal evaluation to demonstrate concepts, even though it might be enormous for things like 9989ADC. It might not be needed, but if applicable, I should calculate exact decimal values if I'm including checks, like how 1.1 equals 44456, which is fairly obvious.Assessing image dimensions and calculations
I'm looking at the task's position, estimating the lower edge at around y=936 and the task line near y=833. The image dimensions are 1536x1152, and it seems like the paper extends to y=934 on the left, and y=936 on the right, with some blank space below. For "развернутая форма," I might need to compute expanded forms for numbers like 44456_10 and "9989ADC," ensuring correct notation and calculations.Exploring number representations
I’m breaking down the integer values and their corresponding exponential notations. For instance, 636 has exponents of 2, 1, and 0, while its fraction part 371 includes -1, -2, and -3. For 132, the integer has exponents 2 down to 0, and the fraction A8C has -1, -2, and -3. I also realize that for 1101, including explicit zero terms in the representation could prevent any omissions. I’ll make sure to simplify the expressions clearly, perhaps using ellipses but making it recognizable.Checking decimal calculations
I'm verifying some decimal calculations to ensure they're accurate. So far, my checks for different bases seem correct. For instance, calculations for 734 in various bases (like octal and hexadecimal) all check out.
I also examine binary operations, and I'm contemplating how to clarify my approach with formats like subscripts and expanded forms. For instance, the fraction in binary and how different conversions translate into decimal values are important. I'm aiming for clear communication in these calculations.Considering base digit mapping
I’m thinking about whether I should include base digit mapping, particularly for the digit D, which represents 13. I wondered if I should calculate decimal for 1.3, but I’m deciding against that. Instead, it seems like the phrase "проверь результат" (verify the result) suggests that I should focus more on verifying the conversion rather than recalculating it. It’s all about making sure the conversions are correct!
Краткий ответ
Нулевые слагаемые в разложениях опущены.
1. Развёрнутая форма целых чисел
\[ 44456_{10}=4\cdot10^4+4\cdot10^3+4\cdot10^2+5\cdot10^1+6\cdot10^0 \]
\[ 53477_{8}=5\cdot8^4+3\cdot8^3+4\cdot8^2+7\cdot8^1+7\cdot8^0 \]
\[ 9989ADC_{16}=9\cdot16^6+9\cdot16^5+8\cdot16^4+9\cdot16^3+ 10\cdot16^2+13\cdot16^1+12\cdot16^0 \]
\[ 111000101001_2=2^{11}+2^{10}+2^9+2^5+2^3+2^0 \]
2. Развёрнутая форма дробных чисел
\[ 23446{,}56_{10}=2\cdot10^4+3\cdot10^3+4\cdot10^2+ 4\cdot10^1+6\cdot10^0+5\cdot10^{-1}+6\cdot10^{-2} \]
\[ 636{,}371_8=6\cdot8^2+3\cdot8^1+6\cdot8^0+ 3\cdot8^{-1}+7\cdot8^{-2}+1\cdot8^{-3} \]
\[ 132{,}A8C_{16}=1\cdot16^2+3\cdot16^1+2\cdot16^0+ 10\cdot16^{-1}+8\cdot16^{-2}+12\cdot16^{-3} \]
\[ 1101{,}01000001_2=2^3+2^2+2^0+2^{-2}+2^{-8} \]
3. Перевод в десятичную систему
\[ 734_8=7\cdot8^2+3\cdot8+4=448+24+4=\boxed{476_{10}} \]
\[ 734_{16}=7\cdot16^2+3\cdot16+4=1792+48+4=\boxed{1844_{10}} \]
\[ 734_9=7\cdot9^2+3\cdot9+4=567+27+4=\boxed{598_{10}} \]
4. Перевод из десятичной системы
- \(436_{10}\)
\[ 436=256+128+32+16+4 \]
\[ \boxed{436_{10}=110110100_2=664_8=1B4_{16}} \]
- \(71_{10}\)
\[ 71=64+4+2+1 \]
\[ \boxed{71_{10}=1000111_2=107_8=47_{16}} \]
5. Действия с двоичными числами
На изображении видны только примеры на сложение и вычитание.
- \[ \begin{array}{r} 1011\\ +0011\\ \hline 1110 \end{array} \qquad \boxed{1011_2+11_2=1110_2} \]
Проверка: \(11+3=14\), а \(14_{10}=1110_2\).
- \[ \begin{array}{r} 101\\ -011\\ \hline 010 \end{array} \qquad \boxed{101_2-11_2=10_2} \]
Проверка: \(5-3=2\), а \(2_{10}=10_2\).
Как запомнить принцип
В разложении числа в системе счисления с основанием \(q\) каждая цифра умножается на степень \(q\), соответствующую её позиции:
\[ a_na_{n-1}\ldots a_0{,}a_{-1}a_{-2} = a_nq^n+\ldots+a_0q^0+a_{-1}q^{-1}+a_{-2}q^{-2}. \]
Цифры шестнадцатеричной системы: \(A=10\), \(B=11\), \(C=12\), \(D=13\). После запятой используются отрицательные степени основания.