Data types — char, short, int, long, float, double, size_t

5.1.2 · Coding › C Programming

Data types EXIST kyun karte hain?

Types KYA hain? (woh 20% jo 80% deta hai)

Formula Typical sizes (LP64, jaise 64-bit Linux/macOS)

Ye standard ke hisaab se minimum-guaranteed hain, lekin actual sizes platform ke hisaab se alag hoti hain.

Type	Typical bytes	Guaranteed min bits	Holds
`char`	1	8	ek byte / character code
`short`	2	16	chhote integers
`int`	4	16	normal integers
`long`	8	32	bade integers
`long long`	8	64	bahut bade integers
`float`	4	— (IEEE-754 single)	~7 decimal digits
`double`	8	— (IEEE-754 double)	~15–16 decimal digits
`size_t`	8 (≈ pointer)	—	object/array sizes (unsigned)

Integer type ki range DERIVE kaise karte hain?

Hum isse first principles se derive karte hain — bit patterns ko count karke.

Unsigned (unsigned char, size_t, …): har pattern ek non-negative value hai. $range = [0, 2^{n} - 1]$ $- 1$ kyun? Kyunki zero $2^{n}$ slots mein se ek kha leta hai, isliye largest value count se ek kam hoti hai.

Signed (two's complement, jo C practically use karta hai): ek bit ki "weight" ko negative banaya jaata hai taaki hum negatives encode kar sakein. Hum $2^{n}$ patterns ko negatives aur non-negatives mein split karte hain: $range = [- 2^{n - 1}, 2^{n - 1} - 1]$

Ye asymmetric kyun hai (positives se ek zyada negative)? Pattern 1000…0 most-negative value ke liye reserved hai; zero positive side par baitha hai, ek positive slot "use kar ke". Isliye tumhe $2^{n - 1}$ negatives milte hain lekin sirf $2^{n - 1} - 1$ positives.

`float`/`double` ek number kaise store karta hai? (IEEE-754)

Formula IEEE-754 number ki value — derived

Ek normalized float represent karta hai: $x = (- 1)^{s} \times (1. f)_{2} \times 2^{e - bias}$ jahan $s$ = sign bit, $f$ = fraction (mantissa) bits, $e$ = stored exponent, aur bias $e$ ko negatives encode karne deta hai.

	sign	exponent	mantissa	bias
`float` (32-bit)	1	8	23	127
`double` (64-bit)	1	11	52	1023

Leading 1 kyun? Normalization form ko $1. xxxx$ fix karta hai isliye leading bit implicit hai — ek free extra bit of precision. Bias kyun? Taaki tiny aur huge dono exponents ek unsigned field mein fit ho sakein bina alag sign ke.

`size_t` kya hai?

Figure — Data types — char, short, int, long, float, double, size_t

Worked example: output predict karo

Worked example Forecast-then-Verify

char c = 200;            // signed char range is [-128,127]
unsigned char u = 200;
printf("%d %d\n", c, u);

Forecast: 200 [-128,127] se bahar hai. Two's complement mein, $200 - 256 = - 56$ , isliye c -56 ban jaata hai. u 200 rehta hai. Kyun? 200 = 1100 1000. Unsigned ke roop mein = 200. Signed ke roop mein, top bit set hai → value = $200 - 256 = - 56$ . Verify (output): -56 200. ✅

Active Recall

Recall Quick self-test (answers cover karo)

$n$ -bit signed integer ki range? → $[- 2^{n - 1}, 2^{n - 1} - 1]$
Woh akela type jiska sizeof standard fix karta hai? → char (== 1)
float ke liye ~7 digits kyun? → 24 mantissa bits × $lo g_{10} 2$
sizeof ka return type? → size_t (unsigned)
0.1+0.2 == 0.3? → false (binary rounding)

n bits se kitne distinct bit patterns exist karte hain?

2^{n}

n-bit unsigned integer ki range?

[0, 2^{n} - 1]

n-bit signed (two's complement) integer ki range?

[- 2^{n - 1}, 2^{n - 1} - 1]

Signed range asymmetric kyun hai (ek zyada negative)?

Pattern 1000…0 most-negative value encode karta hai, aur 0 positive side par ek slot use karke baitha hai.

Signed char (8 bits) ki range?

[- 128, 127]

Unsigned char (8 bits) ki range?

[0, 255]

32-bit int ki range?

[- 2147483648, 2147483647]

Kin type ka sizeof standard ke hisaab se 1 guaranteed hai?

char

C mein integer sizes ki guaranteed ordering?

char ≤ short ≤ int ≤ long ≤ long long

IEEE-754 float bit layout (sign/exp/mantissa)?

1 / 8 / 23, bias 127

IEEE-754 double bit layout?

1 / 11 / 52, bias 1023

Ek normalized IEEE-754 number ki value formula?

(- 1)^{s} \times (1. f)_{2} \times 2^{e - bias}

Float mein ~7 decimal digits of precision kyun hoti hai?

24 mantissa bits × log10(2) ≈ 7.2

Double precision ke approximate decimal digits?

~15–16 (53 bits × log10(2))

size_t kya hai?

Ek unsigned type jo kisi bhi object ka size hold karne ke liye kaafi bada ho; sizeof ke dwara return hota hai.

size_t ke liye printf format specifier?

%zu

"size_t i; i >= 0" countdown loop mein bug kyun hai?

Unsigned kabhi < 0 nahi ho sakta, isliye ye hamesha true hota hai → infinite loop aur wrap-around.

C mein 0.1+0.2 != 0.3 kyun hai?

0.1 aur 0.2 ka koi finite binary representation nahi, isliye unhe round kiya jaata hai.

Recall Feynman: ek 12-saal ke bachche ko samjhao

Choti labelled boxes imagine karo. Ek char box bahut chhota hai — usme ek letter ya ek chhota number fit hota hai. Ek int box bada hai — usme normal counting numbers fit hoti hain. Ek double box special hai: sirf count karne ki jagah, ye number ko "scientific notation" form mein yaad rakhta hai (kuch digits + dot kahan jaata hai), isliye ye bahut bade ya bahut chhote numbers hold kar sakta hai lekin sirf ~15 trustworthy digits ke saath. size_t woh box hai jo hum kehne ke liye use karte hain "ye cheez kitni badi hai?" — aur kyunki kisi cheez ka size kabhi negative nahi hota, woh box sirf 0 aur usse upar hold karta hai. Box par lagaa label computer ko batata hai ki box kitna bada hai aur andar kya hai use kaise padhna hai.

Connections

Two's Complement Representation — kyun signed ranges asymmetric hain
Integer Overflow and Undefined Behaviour — range ke baad kya hota hai
IEEE-754 Floating Point — full mantissa/exponent derivation
sizeof Operator — compile time par sizes kaise query karein
Type Conversion and Promotion — jab types mix hoti hain toh kya hota hai
Pointers and Addresses — kyun size_t pointer width se match karta hai