0.1 IEEE 754 mein exactly store kyun nahi hota?

0.1 binary mein ek repeating fraction hai, bilkul jaise 1/3 decimal mein hai, isliye use finite number of bits mein nahi likha ja sakta. Converter use nearest representable value par round karta hai aur bacha hua rounding error dikhata hai.

32-bit aur 64-bit floating point mein kya farq hai?

32-bit (single / float) lagbhag 7 decimal digits precision ke liye ek 8-bit exponent aur 23-bit mantissa use karta hai. 64-bit (double) lagbhag 15–16 digits ke liye 11 aur 52 bits use karta hai. Ek hi number ko dono mein compare karne ke liye precision toggle karein.

Sign, exponent aur mantissa fields main kaise padhoon?

Pehla bit sign hai (0 positive, 1 negative). Agle 8 ya 11 bits exponent hain, jo 127 ya 1023 ke bias ke saath store hote hain. Baaki 23 ya 52 bits mantissa hain — normal numbers ke liye ek implicit leading 1 ke baad ka fraction.

Infinity, NaN aur negative zero kaise encode hote hain?

Zero mantissa ke saath ek all-ones exponent ±Infinity hai; non-zero mantissa ke saath yeh NaN hai. Negative zero sign bit ke alawa saare zeros hote hain. Tool in har special case ko aapke enter karte hi label karta hai.

Kya main ek hex float value ko wapas decimal mein convert kar sakta hoon?

Haan. IEEE 754 → Decimal par switch karein, Hex ya Binary chunein, aur pattern paste karein. Tool sign, exponent aur mantissa ko dobara banata hai aur woh exact decimal dikhata hai jo bits represent karte hain.

Subnormal (denormal) number kya hota hai?

Jab exponent field saare zeros ho lekin mantissa na ho, to number subnormal hota hai: yeh sabse chhote normal float se chhoti values represent karne ke liye implicit leading 1 ko drop kar deta hai, kam precision par. Tool inhe automatically flag karta hai.

IEEE 754 Floating Point Converter

Decimals ko 32-bit aur 64-bit IEEE 754 mein aur wapas badlein — sign, exponent aur mantissa bits, hex, exact stored value, aur rounding error ke saath, sab aapke browser mein.

IEEE 754 Converter poori tarah aapke browser mein standard number APIs se chalta hai. Jo decimals, hex aur bit patterns aap convert karte hain woh aapke device par rehte hain aur kabhi ArrayKit ko upload nahi hote.

Number Base Converter kholein

IEEE 754 Converter ke baare mein

IEEE 754 Converter ek decimal number ko uske exact 32-bit (single) aur 64-bit (double) floating-point representation mein badal deta hai. Yeh sign bit, biased exponent aur mantissa ko alag colour-coded bit fields ke roop mein dikhata hai, saath hi hexadecimal word, woh exact value jo bits asal mein store karte hain, aur jo aapne type kiya aur machine jo rakhti hai uske beech ka rounding error. Kyunki binary zyadatar decimal fractions ko represent nahi kar sakta, 0.1 jaisi values thodi si drift karti hain — yeh tool us drift ko dikha deta hai. Doosri taraf bhi kaam karein: ek hex pattern ya ek raw bit string paste karein aur jis decimal mein woh decode hota hai use recover karein. Yeh float precision debug karne wale, float32 ko float64 se compare karne wale, ya Infinity, NaN aur denormals inspect karne wale developers ke liye bana hai. Har conversion locally aapke browser mein chalta hai; jo numbers aap enter karte hain woh kabhi aapke device se bahar nahi jaate.

Features

Kisi bhi decimal ko 32-bit (single) aur 64-bit (double) IEEE 754 mein convert karein
Colour-coded sign, exponent aur mantissa bit fields
Poore binary bit string ke saath hex word dikhata hai
Exact stored value aur aapke input ke muqaable rounding error batata hai
Reverse mode ek hex pattern ya bit string ko wapas decimal mein decode karta hai
Infinity, NaN, negative zero aur subnormal (denormal) numbers ko handle karta hai
Biased aur unbiased exponent dikhata hai taaki aap scale padh sakein
Poori tarah aapke browser mein chalta hai — numbers kabhi aapke device se bahar nahi jaate

IEEE 754 Converter kaise use karein

Decimal → IEEE 754 selected rakhein aur 0.1 jaisa ek number type karein
Single- ya double-precision bits dekhne ke liye 32-bit ya 64-bit chunein
Sign, exponent aur mantissa fields, hex, aur rounding error padhein
IEEE 754 → Decimal par switch karein aur wapas decode karne ke liye ek hex ya binary pattern paste karein

Example

Input

0.1  (as float32)

Output

hex:            0x3dcccccd
stored value:   0.10000000149011612
exact value:    0.100000001490116119384765625
rounding error: 1.4901161193847656e-9

0.1 ka koi exact binary form nahi hota, isliye float32 0.1 se thodi si badi value store karta hai.

Common errors aur troubleshooting

Do numbers jo barabar hone chahiye code mein alag compare hote hain. — Rounding har operation par alag hoti hai, isliye floats ko == ke bajaye ek chhote tolerance (epsilon) se compare karein, ya zyada precision ke liye 64-bit par jaayein.
Ek paste kiya hex value unexpectedly Infinity ya NaN mein decode hota hai. — Ek all-ones exponent field ka matlab Infinity (zero mantissa) ya NaN (non-zero mantissa) hai. Width bhi check karein — 32-bit ke liye 8 hex digits, 64-bit ke liye 16.
Aapke program mein 0.1 + 0.2 0.3 ke barabar nahi hota. — Har value pehle nearest binary float par round hoti hai, isliye sums alag ho jaate hain. Mismatch ke peeche ki exact stored values dekhne ke liye 0.1, 0.2 aur 0.3 yahan convert karein.
Ek bahut chhota number 'subnormal' label hota hai. — Sabse chhote normal exponent ke neeche, floats implicit leading 1 ko drop kar dete hain aur subnormal (denormal) encoding use karte hain, zero ke kareeb pahunchne ke liye precision ka trade karke.

Aksar pooche jaane wale sawaal

0.1 IEEE 754 mein exactly store kyun nahi hota?: 0.1 binary mein ek repeating fraction hai, bilkul jaise 1/3 decimal mein hai, isliye use finite number of bits mein nahi likha ja sakta. Converter use nearest representable value par round karta hai aur bacha hua rounding error dikhata hai.
32-bit aur 64-bit floating point mein kya farq hai?: 32-bit (single / float) lagbhag 7 decimal digits precision ke liye ek 8-bit exponent aur 23-bit mantissa use karta hai. 64-bit (double) lagbhag 15–16 digits ke liye 11 aur 52 bits use karta hai. Ek hi number ko dono mein compare karne ke liye precision toggle karein.
Sign, exponent aur mantissa fields main kaise padhoon?: Pehla bit sign hai (0 positive, 1 negative). Agle 8 ya 11 bits exponent hain, jo 127 ya 1023 ke bias ke saath store hote hain. Baaki 23 ya 52 bits mantissa hain — normal numbers ke liye ek implicit leading 1 ke baad ka fraction.
Infinity, NaN aur negative zero kaise encode hote hain?: Zero mantissa ke saath ek all-ones exponent ±Infinity hai; non-zero mantissa ke saath yeh NaN hai. Negative zero sign bit ke alawa saare zeros hote hain. Tool in har special case ko aapke enter karte hi label karta hai.
Kya main ek hex float value ko wapas decimal mein convert kar sakta hoon?: Haan. IEEE 754 → Decimal par switch karein, Hex ya Binary chunein, aur pattern paste karein. Tool sign, exponent aur mantissa ko dobara banata hai aur woh exact decimal dikhata hai jo bits represent karte hain.
Subnormal (denormal) number kya hota hai?: Jab exponent field saare zeros ho lekin mantissa na ho, to number subnormal hota hai: yeh sabse chhote normal float se chhoti values represent karne ke liye implicit leading 1 ko drop kar deta hai, kam precision par. Tool inhe automatically flag karta hai.

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