Re:CS50

간만에 CS50을 다시 본다

네이버 부스트캠프 참여해서 에너지 좀 얻으려고 시험 준비겸 보는데

갑자기 뇌속 정리 좀 하고 싶어졌음

Binary Digit ( bit )

Byte

2 Bytes

4 Bytes

8 Bytes

Float

Double

AOB(Array of Byte)

 

below, Stack overflow answers for the record

1st answer

In C, an int and float each take up 4 bytes, or 32 bits, in memory. The difference between int and float is not the number of bits they take up in memory, but rather in the way the ALU (Arithmetic Logic Unit) treats each number. An int is treated as the integer represented by its bits using two's complement notation. A float, on the other hand, is encoded (typically in IEEE 754 format) to represent a number in exponential form (e.g. 2.9979245x108 is a number in exponential form with base 2.9979245 and exponent 8). The number of significant digits in the decimal representation of a floating point number is always about the same: 6-9 digits for 32-bit float and 15-17 digits for a 64-bit float (or double). For example, the value 4.2949673x109 is what I get as the decimal representation of the closest 32-bit float to the number 232 , and it has 8 significant digits.

It can be a common misconception that a floating point number somehow represents more information than a fixed-point number, which is not true. While a 32-bit float can represent numbers of greater magnitude than a 32-bit int, it cannot represent all of them with as much precision. In total, this answer derives that a 32-bit float can represent around 4,278,190,081 unique numbers. This other answer contains a nice plot showing how these 32-bit floats are distributed on the real line.

While an int may not be able to represent numbers with as large of a magnitude as a float, it represents each number in its valid range (-232 to 232-1) with the same precision. The largest number it can represent is 2,147,483,647 and has 10 significant digits. And in total, it can represent 232=4,294,967,296 unique numbers, which is more than for the 32-bit float!

 2nd answer

In fact, the length of a certain data type differs on platforms. Yet let us say now float and int are same, 4 bytes.

4 Bytes equal 32 bits, and in binary, the range is

00000000000000000000000000000000

to

11111111111111111111111111111111

At this point, we should recall geometric sequence, the sum above equals

2^32 + 2^31 + ... + 2^1 + 2^0 = 2147483648

Notice, C redfines the range from math to language, as unsigned or signed via shift.

That is to say it can also define float.

SEEEEEEEEMMMMMMMMMMMMMMMMMMMMMMM

S = sign (1 bit)

E = exponent (8 bits)

M = mantissa (23 bits)

The value calculation follows IEEE-754, which is not easy, but we can try at 754 converter :)

Now, the range, (see the exponent trick? It means E-127, minus!)

0 00000001 00000000000000000000000

to

0 11111110 11111111111111111111111

From math,

2^-126 * 1.00000000000000000000000 = 1.1754943508222875 × 10^-38

to

2^(128) * 1.11111111111111111111111 = 3.7809151880104275 x 10^38

Notice there is a hidden 1 for mantissa, otherwise you always get 0 :<

At last machines are built for saving life at the very begining, so before we choose the data type, we better checkout the range, from the header files, e.g.

#include <stdio.h>
#include <limits.h>
#include <float.h>

int main()
{
    printf("Range of signed char %d to %d\n", SCHAR_MIN, SCHAR_MAX);
    printf("Range of unsigned char 0 to %d\n\n", UCHAR_MAX);

    printf("Range of signed short int %d to %d\n", SHRT_MIN, SHRT_MAX);
    printf("Range of unsigned short int 0 to %d\n\n", USHRT_MAX);

    printf("Range of signed int %d to %d\n", INT_MIN, INT_MAX);
    printf("Range of unsigned int 0 to %lu\n\n", UINT_MAX);

    printf("Range of signed long int %ld to %ld\n", LONG_MIN, LONG_MAX);
    printf("Range of unsigned long int 0 to %lu\n\n", ULONG_MAX);

    // In some compilers LLONG_MIN, LLONG_MAX
    printf("Range of signed long long int %lld to %lld\n", LLONG_MIN, LLONG_MAX); 
    // In some compilers ULLONG_MAX
    printf("Range of unsigned long long int 0 to %llu\n\n", ULLONG_MAX); 

    printf("Range of float %e to %e\n", FLT_MIN, FLT_MAX);
    printf("Range of double %e to %e\n", DBL_MIN, DBL_MAX);
    printf("Range of long double %e to %e\n", LDBL_MIN, LDBL_MAX);

    return 0;
}

 

 

--

2^8 = 256, 255 cuz start it from 0

Unicode - http://home.unicode.org/

Home

ZWNJ(ZERO WIDTH NON-JOINER), Emoji joiner, U+200D

 

Words that i didn't know

reconcile

 

RGB 2^8, 255

RGB 255, 255, 255

three 2^8, 24 bit, represents BPP, Color depth

 

refers : IEEE 754 standard: binary32