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question:Another way to think about this, is to consider MSB as having weight of -1 * 2^(n-1), assuming there are n bits for this number.
answer:Yes, that's a very insightful and correct way to interpret the most significant bit (MSB) in a two's-complement system. In an n-bit two's-complement number, the MSB does indeed have a "negative weight." This means while all other bits have regular positive weights associated with their place values, the MSB has a negative place value. For an n-bit number, the bit weights from the least significant bit (LSB) to the most significant bit (MSB) are: 2^0, 2^1, 2^2, ..., 2^(n-2), -2^(n-1) The negative weight of the MSB allows it to represent negative numbers naturally within the binary system without the need for an additional sign indicator. This is how negative numbers are encoded, where the presence of a '1' in the MSB position indicates that the weight is subtracted from the sum of the weights of the other bits. Let's see an example with 4 bits: Suppose we have the binary number `1001`. In a two's-complement 4-bit system, the place value of each bit would be: - MSB: 2^(4-1) = 2^3 = 8, but with negative weight: -8 - Next bit: 2^(3-1) = 2^2 = 4, positive weight - Next bit: 2^(2-1) = 2^1 = 2, positive weight - LSB: 2^(1-1) = 2^0 = 1, positive weight So, the decimal value of `1001` is: (-2^(3)) * 1 + (2^2) * 0 + (2^1) * 0 + (2^0) * 1 = -8 * 1 + 4 * 0 + 2 * 0 + 1 * 1 = -8 + 0 + 0 + 1 = -7 By viewing the MSB as having a negative weight, the two's-complement representation allows us to perform regular binary addition, yet correctly handle the arithmetic of both positive and negative integers.
question:Because the quantity of negative numbers is more than positive numbers, so we can not simply do -a on negative number a and assume it won't overflow.
answer:That's correct. In an n-bit two's-complement system, negative numbers have one more value than positive numbers. Specifically, the range is from -2^(n-1) to 2^(n-1) - 1. The asymmetry arises because the `0` is included in the positive side of the range. This means that in an 8-bit system, you can represent numbers from -128 to +127. If you were to naively try to calculate the two's complement negative of -128 (10000000 in binary), you would follow the process of inverting the bits to get 01111111 and then adding 1. However, 01111111 is already the binary representation for the maximum positive number, +127. Adding one to this number leads to an overflow that recycles back to the minimum negative number -128, effectively leaving the original number unchanged: ``` 01111111 (binary for +127) +00000001 (binary for 1) --------- 10000000 (binary for -128, overflow occurs) ``` This overflow event means that you can't just flip the sign of the most negative number without going outside the bounds of the fixed-width number system. As such, the bit pattern `10000000` in an 8-bit two's-complement system is a special case — it is its own negative. This is a consequence of having one more negative value than positive values in this encoding scheme. In practice, this situation leads to what is referred to as integer overflow, and it's a condition that usually has to be handled by software (e.g., with exception handling or by using wider integers for calculations) to avoid unexpected results or software bugs.
question:Какая норма расхода топлива Haval H6, AT, 1.5 л, 143 л.с. ?
answer:Согласно официальным данным производителя, Haval H6 AT с двигателем объемом 1.5 литра и мощностью 143 лошадиных сил имеет средний расход топлива около 7,0-8,0 литров на 100 километров в смешанном режиме эксплуатации.
question:Что влияет на расход топлива?
answer:Расход топлива автомобиля может быть оказан влиянием следующих факторов: 1. Стиль вождения: агрессивное ускорение, частое торможение и высокая скорость могут увеличить расход топлива. 2. Вес автомобиля: более тяжелые автомобили требуют больше топлива для движения. 3. Состояние дороги: езда по хорошо уложенным и ровным дорогам с меньшими препятствиями может снизить расход топлива. 4. Качество топлива: использование некачественного топлива может привести к увеличению расхода. 5. Тип и состояние двигателя: старые или неисправные двигатели могут потреблять больше топлива. 6. Давление в шинах: неправильное давление в шинах может привести к увеличению сопротивления качению и увеличению расхода топлива. 7. Погодные условия: езда в городских условиях с постоянными пробками, езда в гору или в штормовые погодные условия может повысить расход топлива. Это некоторые из факторов, которые могут влиять на расход топлива, их влияние может незначительно различаться в зависимости от модели автомобиля.