A "bit" is the smallest unit of data and information storage in computing. The term "bit" is a contraction of "binary digit." It can have one of two possible values: 0 or 1, representing the two states of a binary system, which is the foundation of digital computing
- What is a
Byte? - What is
LSbandMSb?
A machine only treats a number by binary number Where is human to understand a number by base 10.
Terms
If the base is 2, 8, 10, and 16, there is a specific name for each base. The base 2 is binary. What are rest of them?
- Base 2: binary
- Base 8: ?
- Base 10: ?
- Base 16: ?
Representation
Sometimes you will see some symbol like 0b****** or 0x****. What are these? Explain them with examples.
How do you convert base 10 number to base 2 (binary) number? Write an algorithm for it.
function convertToBase2(numBase10: number): [number] {
// e.g, If the `num` is 11, it should return [1,0,1,1]
}How do you convert base 2 number to base 10 number? Write an algorithm for it.
function convertToBase10(numBase2: [number]): number {
// e.g, If the `numBase2` is [1,0,1,1], it should return 11
}How do you convert base 10 number to base 3 number? Write an algorithm for it.
function convertToBase3(numBase10: number): [number] {
// e.g, If the `num` is 11, it should return [1,0,2]
}How do you convert base 10 number to base 16 number? Write an algorithm for it.
function convertToBase16(numBase10: number): string {
// e.g, If the `num` is 2894, it should return "B4E".
}🚀 For each answer, describe the steps and processes you followed e.g, Answer format
Step 1. ****
Step 2. ****
Step 3. ***
Thus, the answer is ****Bits can represent an integer. An integer is one of the privative data type of programming language.
What is the range of 8 bits integer.?
You don't have to consider a negative number. We call this data type especially an unsigned integer.
An unsigned integer starts from zero.
What is the range of 32 bits unsigned integer?
We also want to represent a negative number by using bits.
When a integer can treat both negative and positive number, we call this type singed integer. There are several ways to make a negative integer. One of the common way is "Two's complement"
Calculate the binary representation of the 8-bit signed integer -7 using the "Two's complement" method. Outline the steps and processes you followed.
Calculate the binary representation of the 32-bit signed integer -7 using the "Two's complement" method.
Calculate the binary representation of the 32-bit signed integer -239,472,903 using the "Two's complement" method.
Convert the binary value 11010101 into an 8-bit signed integer representation using the "Two's complement" method.
Masaki likes to play retro tv games👾. One day he was playing one of the RPG games🗡️. He finally faced the last boss 😈 and the boss's HP (hit point) was a maximum of HP 32,000. Masaki was excited but he'd wrongly casted a spell of healing the HP (increasing the HP) ❤️🩹 to the Boss instead of a fire attack🧙♂️. The boss got healed by + HP 1,000.
However, as soon as the boss got healed, it got died and defeated😇. Can you assume and explain what happened? 😁
One of the Answers: Integer overflow
Bitwise operations are fundamental operations performed on individual bits (binary digits) within a binary representation of data.
There are mainly six common bitwise operations. List up all of them with example.
and what are time complexity of all bitwise operations?
What are the benefits of using bit operations?
How do you write a code that determines that if the input number is odd or even?
Can you write a code without using any math operators +, -, *, /? 😁
Constraints:
- input: 32 bit signed integer
function isOdd(input: number): bool {
}Can you write a code which multiplies the input number by 2 and 4 without using *? 😁
Constraints:
- input: 32 bit unsigned integer
- You don't have to care about integer overflow
function multiplyByTwo(input: number): number {
}function multiplyByFour(input: number): number {
}Can you write a code which divides the input number by 2 or 4 without using /? 😁
Constraints:
- input: 32 bit unsigned integer
- The result will be always round down
- You don't have to care about integer overflow
function divideByTwo(input: number): number {
}function divideByFour(input: number): number {
}Write a code which inverts the sign of number.
e.g, invertSign(3) -> -3, invertSign(-6) -> 6
Can you write the code without using - nor *? 😁
Constraints:
- input: 32 bit signed integer
function invertSign(input: number): number {
}Do not use a build in library such as count bits
- https://leetcode.com/problems/number-of-1-bits/
- https://leetcode.com/problems/hamming-distance/submissions/
- https://leetcode.com/problems/single-number/
- https://leetcode.com/problems/power-of-two/
Write a code which set the specific n th digit to 1.
e.g,
- input: 0 (Ob00000000), digit: 2 -> return: 4 (0b00000100)
- input: 89 (Ob01011001), digit: 5 -> return: 121 (Ob01111001)
Constraints:
- input: 32 bit signed integer
- 0 < digit < 32
function setBit(input: number, digit: number): number {
}Write a code which clear the specific n th digit to 1.
e.g,
- input: -1 (Ob11111111), digit: 3 -> return: 9 (Ob11110111)
- input: 89 (Ob01011001), digit: 6 -> return: 25 (Ob00011001)
Constraints:
- input: 32 bit signed integer
- 0 < digit < 32
function clearBit(input: number, digit: number): number {
}Masaki joined a game project in the company👾. The game is a retro RPG and has a very massive content. Thus, there are many flags to manage⛳. However, the game is very old and the company wants to minimize the game size as much as possible.
There are about 1,000 flags you have to manage in the game. Each flag is a boolean type which takes 1 byte to allocate. If it is required to use only 150 bytes for flag management, how do you design it? How do you check and update a flag?🤔