The number system having the largest base is the ______ number system.
hexadecimal
Number System Bases Explained
Understanding different number systems is crucial in computing and mathematics. Each number system uses a specific set of symbols (digits) and has a 'base' or 'radix' that determines how numbers are represented. The base essentially indicates the total count of unique digits available in that system. Let's look at the bases of the number systems mentioned in the options:
Comparing Number System Bases
We need to identify the number system with the largest base among the given choices:
- Binary Number System: This system uses only two digits, 0 and 1. Therefore, its base is 2. We represent this base using LaTeX as $2$.
- Octal Number System: This system uses eight digits, ranging from 0 to 7. Its base is 8, represented in LaTeX as $8$.
- Decimal Number System: This is the system we use in everyday life. It employs ten digits, from 0 to 9. Its base is 10, written in LaTeX as $10$.
- Hexadecimal Number System: This system uses sixteen symbols: the digits 0 through 9 and the letters A through F (representing values 10 through 15). Its base is 16, which we write in LaTeX as $16$.
Identifying the Largest Base
Comparing the bases we've identified:
| Number System | Digits Used | Base |
|---|---|---|
| Binary | 0, 1 | $2$ |
| Octal | 0-7 | $8$ |
| Decimal | 0-9 | $10$ |
| Hexadecimal | 0-9, A-F | $16$ |
By comparing the values $2$, $8$, $10$, and $16$, it is clear that $16$ is the largest value.
Therefore, the number system having the largest base among the options is the hexadecimal number system.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
