How high can we count with an unsigned 16-bit integer?

How high can we count with an unsigned 16-bit integer?

A 16-bit integer can store 216 (or 65,536) distinct values. In an unsigned representation, these values are the integers between 0 and 65,535; using two’s complement, possible values range from −32,768 to 32,767.

How do you find the number of 1 bits in an integer?

So if we subtract a number by 1 and do it bitwise & with itself (n & (n-1)), we unset the rightmost set bit. If we do n & (n-1) in a loop and count the number of times the loop executes, we get the set bit count.

How do you count the number of 1s of a number?

The algorithm to count the number of 1s in Given Bit Sequence

1. set the loop counter to zero to start with.
2. loop until number > 0. — clear the least significant bit of number: number &= (number-1) — increment the loop counter by 1: count++;
3. return the loop counter.

What is the maximum value representable by a signed 16-bit integer?

65,535
To an unsigned short? Solution Since 15 bytes are used to represent a short, with the 16th bit used for the sign, the largest number it can represent is 215 − 1 = 32,767. For an unsigned short, all 16 bits are used to represent the value, so the largest representable number is 216 − 1 = 65,535.

What is the range of 16-bit signed integer?

-32,768 to +32,767
Signed Integer: A 16-bit signed integer ranging from -32,768 to +32,767.

What are the maximum and minimum values that can be stored in a short 16-bit signed integer?

short: The short data type is a 16-bit signed two’s complement integer. It has a minimum value of -32,768 and a maximum value of 32,767 (inclusive).

Which register is 16-bit?

A 16-bit Data Segment register or DS register stores the starting address of the data segment. Stack Segment − It contains data and return addresses of procedures or subroutines. It is implemented as a ‘stack’ data structure. The Stack Segment register or SS register stores the starting address of the stack.

How to count the number of set bits in an integer?

Depending on how many bits are set on average it may be faster or slower than the kerrigan loop – though probably also depends on the used CPU. A more optimized way (from commenters link above): If you are using GCC, use the builtin function int __builtin_popcount (unsigned int x). On some machines, this will reduce to a single instruction.

How to unset the rightmost set bit in an integer?

Brian Kernighan’s Algorithm: Subtracting 1 from a decimal number flips all the bits after the rightmost set bit (which is 1) including the rightmost set bit. So if we subtract a number by 1 and do bitwise & with itself (n & (n-1)), we unset the rightmost set bit.

Can a 32 bit integer be hard coded?

This is hard-coded to 32 bit integers, if yours are a different size it will need adjusting. Turns out there are some pretty sophisticated ways to compute this as answered here.

Which is the rightmost set bit in subtracting a number?

Brian Kernighan’s Algorithm: Subtracting 1 from a decimal number flips all the bits after the rightmost set bit (which is 1) including the rightmost set bit. So if we subtract a number by 1 and do it bitwise & with itself (n & (n-1)), we unset the rightmost set bit.