C++ primer 5th edition: A bitset to represent a sequence of integers

Question

I am asked on C++ primer 5th edition this exercise:

Exercise 17.10: Using the sequence 1, 2, 3, 5, 8, 13, 21, initialize a bitset that has a 1 bit in each position corresponding to a number in this sequence. Default initialize another bitset and write a small program to turn on each of the appropriate bits.

In fact I almost solved all the exercises of the book but I couldn't understand this. I've understood std::bitset.

I've found a solution like this:

// init from the sequence: 1, 2, 3, 5, 8, 13, 21
std::bitset<22> bitseq("1000000010000100101110");
std::cout << bitseq << std::endl;

// Default initialize, then turn on.
std::bitset<22> bit_default;
for (auto i : {1, 2, 3, 5, 8, 13, 21})
    bit_default.set(i);
std::cout << bit_default << std::endl;

assert(bitseq == bit_default);

But I don't know how it is this way and how it works? please help me to understand this if it is correct. Thanks guys too much!

I don't understand how can such 1000000010000100101110 represent the sequence 1, 2, 3, 5, 8, 13, 21?.

Did you write that code yourself? Then you should already understand it. There's nothing tricky about it. — Mark Ransom, Jan 12 '21 at 20:53
@MarkRansom: No it is not me who wrote it I've found it as a solution. — Maestro, Jan 12 '21 at 20:54
Which bit (pardon the pun) don't you understand: the `auto`, the `.set(i)` or something else? — Adrian Mole, Jan 12 '21 at 20:55
Can you be more specific about the part you don't understand? — Mark Ransom, Jan 12 '21 at 20:55
@AdrianMole: How can `1000000010000100101110` represent the sequence `1, 2, 3, 5, 8, 13, 21`? — Maestro, Jan 12 '21 at 20:57
It doesn't. That's not what the book is asking. It's stating that in a `bitset<22>`, the bits `1, 2, 3, 5, 8, 13, 21` should be set to `1` — NathanOliver, Jan 12 '21 at 20:58
Count the positions of each of the `1` characters, starting from the right, and counting from zero. — Adrian Mole, Jan 12 '21 at 20:58
It seems the exercise text specifically explains what you're asking about. In the context of the exercise, each number in the sequence is a bit position in your bitset, where the bit is set to 1... — Asteroids With Wings, Jan 12 '21 at 21:04
@NathanOliver Being picky, that is a valid representation of that sequence. — Asteroids With Wings, Jan 12 '21 at 21:05

KamilCuk · Accepted Answer · 2021-01-12T21:10:09.853

How can 1000000010000100101110 represent the sequence 1, 2, 3, 5, 8, 13, 21?

Numbers in base 2 are typically written MSB first - most significant bit first - and typically numbered or indexed from right to left, from the least significant bit, starting from 0 (or 1).

1000000010000100101110
^       ^            ^-- bit with index 0  - least significant bit 2^0
^       ^           ^--- bit with index 1
^       ^          ^---- bit with index 2
^       ^         ^----- bit with index 3
^       ^        ^------ bit with index 4
^       ^       ^------- bit with index 5
^       ^      ^-------- bit with index 6
^       ^     ^--------- bit with index 7
^       ^--------------- bit with index 13
^----------------------- bit with index 21 - most significant bit 2^21

When numbering bit positions starting from 0 from the right side, the sequence 1, 2, 3, 5, 8, 13, 21 represents set bits within the string 1000000010000100101110.

So I can start from `1` rather than `0` to be something like this `100000001000010010111`? — Maestro, Jan 12 '21 at 21:05
Let's a real life example: When you __index__ the number of shoes, in real life you count: 1st shoe. 2nd shoe. 3rd shoe. In programming arrays start from 0: shoe __number 0__ is the first shoe, shoe _number_ 1 is the second shoe, etc. You can __index__ the bit positions starting from 1, but usually it's confusing, as array indexing starts from 0, and bitshifts work like `1<<4` is the 5th (not 4rd!) bit from the right. — KamilCuk, Jan 12 '21 at 21:07

C++ primer 5th edition: A bitset to represent a sequence of integers

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