Instruction formats and encoding: Foundations — Hinglish deep dive

5.1.2 · D1 · Hardware › Instruction Set Architecture (ISA) › Instruction formats and encoding

Is page pe assume kiya gaya hai ki tumne pehle kuch nahi dekha. Hum har woh symbol build karenge jo parent note Instruction formats and encoding mein use hota hai — ek ek karke, har ek ko ek picture se anchor karke, har ek ko use karne se pehle earn karke. Yahan kuch bhi memorise nahi karna; sab kuch derive hota hai.

0. Sabse basic object: ek bit

Figure s01 neeche aath bulbs ki ek row draw karta hai: jale hue bulbs (butter-yellow) 1 hain, dim grey bulbs 0 hain. Sabse baayi taraf ka bulb dekho — woh ek bit hai, aur chhota arrow us par point karta hai. Neeche ki green line saare aath bulbs ko bracket karti hai; us grouping ko hum abhi ek second mein byte kahenge.

Figure — Instruction formats and encoding

1. Bits ka ek group: binary numbers aur $2^{b}$

Agar ek bit 2 possibilities hold karta hai, toh $b$ bits ka ek group kitna hold karta hai?

Ek bit add karo → har purana pattern ab 0 ya 1 mein end ho sakta hai → patterns ki sankhya double ho jaati hai. Toh:

1 bit → 2 patterns
2 bits → 4 patterns
3 bits → 8 patterns
$b$ bits → $2^{b}$ patterns.

Figure s02 isko ek bar chart mein dikhata hai: har bar pichle se do ke factor se ooncha hai, aur bars ke beech coral arrows kehte hain "×2 again". Woh visual doubling hi $2^{b}$ ka matlab hai.

Bit pattern se actual number tak: positional weights

Hum kehte rehte hain " $10110$ ek number hai" — chaliye isko earn karte hain, kyunki poora topic isi par lean karta hai.

$10110$ lo (paanch bits). Right se positions line karo:

$2^{4} = 16 1 2^{3} = 8 0 2^{2} = 4 1 2^{1} = 2 1 2^{0} = 1 0$

Jahan bit $1$ hai wahan weights add karo: $16 + 4 + 2 = 22$ .

2. Ulta sawaal: $lo g_{2}$ aur ceiling $⌈ ⌉$

Parent note likhta hai $b = ⌈ lo g_{2} N ⌉$ . Chaliye har symbol earn karte hain.

Woh sawaal jo hum actually pooch rahe hain: "Mere paas $N$ alag cheezein hain (maan lo 32 registers). Mujhe kitne bits $b$ chahiye taaki $2^{b}$ kam se kam $N$ ho?"

Lekin $lo g_{2} 100 = 6.64 \dots$ — tum 6.64 switches nahi rakh sakte. Bits poore hote hain, aur 6 bits ( $= 64$ patterns) kaafi nahi hain. Hum round up karke 7 karna chahenge.

Figure s03 ek line par $2^{5} = 32$ , $2^{6} = 64$ , $2^{7} = 128$ rakhta hai aur "need 100" par ek coral marker drop karta hai. Tum dekh sakte ho 64 marker ke left mein baithta hai (too few) aur 128 right mein (fits), toh jawab $6.64$ se round up karke $7$ hona chahiye.

3. Bits ka ek named group: ek field

Fields name karne se pehle hum agree karna chahte hain ki bit positions kaise count karein — warna "bits 0 through 6" ambiguous hai.

Figure s04 32-bit word ko chhah rounded, pastel boxes ke roop mein draw karta hai. Neeche ke labels dekho: "high bits (left)" aur "bit 0 (right)" — yahi hamari convention visible ho rahi hai. Coral opcode box far right mein baithta hai (bits 0–6); arrow yaad dilata hai ki decoder pehle wahan dekhta hai.

Do field-names jinpe parent lean karta hai:

opcode — "kya kaam" field (add? jump? load?). Hamesha same position mein taaki decoder pehle ise dhundh sake.
operand fields — "kya usse karna hai": register numbers, ya ek immediate.

4. Do special operands: register aur immediate

$32$ registers $\Rightarrow b = ⌈ lo g_{2} 32 ⌉ = 5$ bits per register field. Woh "5" jo baar baar dikhta hai woh magic nahi hai — yeh 32 pe apply kiya gaya Section 2 hi hai.

5. Negative immediates: two's complement aur sign extension

addi x1, x2, -8 kaam karna chahiye, isliye ek field ko ek negative number mean karne mein capable hona chahiye.

Section 1 ke positional weights se build karte hain. Ek unsigned $b$ -bit number mein har bit ka weight $+ 2^{i}$ hota hai. Two's complement exactly ek cheez change karta hai: top bit ka weight negative ho jaata hai, $- 2^{b - 1}$ , jabki har lower bit apna usual $+ 2^{i}$ rakhta hai.

4 bits pe dekho ( $b = 4$ , toh top weight $- 2^{3} = - 8$ hai):

$1000 = - 8, 1111 = - 8 + 4 + 2 + 1 = - 1, 0111 = 4 + 2 + 1 = + 7.$

Range phir weights se sidha nikalta hai. Most negative value sirf top bit on karti hai: $1000 \dots 0 = - 2^{b - 1}$ . Most positive top bit chhor ke har bit on karta hai: $0111 \dots 1 = 2^{b - 1} - 1$ . Toh:

$range = - 2^{b - 1} to 2^{b - 1} - 1.$

Parent ke 12-bit immediate ke liye: $- 2^{11}$ to $2^{11} - 1 = - 2048$ to $+ 2047$ . Full treatment ke liye Two's Complement and Sign Extension dekho.

6. Symbols ko ek saath rakhna

Ab parent ke tally mein har symbol sight pe samajh mein aata hai:

$7 f u n c t 7 5 r s 2 5 r s 1 3 f u n c t 3 5 r d 7 o p co d e = 32 bits$

$7, 5, 5, 3, 5, 7$ bits mein field widths hain (Section 3).
Har $5$ aaya $⌈ lo g_{2} 32 ⌉$ se (Sections 2 & 4).
Sum exactly $32$ hona woh fixed budget hai jis par parent bar bar stress karta hai.

Related building topics jinpe tum ab approach kar sakte ho: Addressing Modes (operand fields memory kaise name karte hain), RISC vs CISC (fixed vs variable width philosophy), Pipelining (kyun fast fixed decode matter karta hai).

Prerequisite map

Equipment checklist

Har jawab reveal karne se pehle zyaor se bolo.

Ek bit mein kitne possible values store hote hain

Exactly two — 0 ya 1.

Ek byte mein aur yahan ek word mein kitne bits hote hain

Ek byte 8 bits ka hai; ek word 32 bits (4 bytes) ka hai in machines par.

b

bits mein kitne distinct patterns fit hote hain

2^{b}

Binary

10110

kaun sa number hai, aur kaise

16 + 4 + 2 = 22

, position weights

2^{i}

sum karke jahan bit 1 hai.

Bit 0 kaun si end par hota hai

Rightmost (lowest-weight,

2^{0}

) bit par; higher indices baayi taraf jaate hain.

lo g_{2} N

kaun sa sawaal answer karta hai

"2 ko kisi power pe uthane se

N

milta hai?" — yeh

2^{b}

ko undo karta hai.

b = ⌈ lo g_{2} N ⌉

mein ceiling

⌈ ⌉

kyun

Bits whole numbers hote hain, isliye hum round up karte hain taaki

2^{b} \geq N

ho.

N = 1

ke liye formula kya deta hai

b = 0

— ek zero-width field, kyunki ek choice mein koi information nahi hoti.

32 registers index karne ke liye kitne bits chahiye

⌈ lo g_{2} 32 ⌉ = 5

Field kya hoti hai

Instruction word ka ek fixed, named slice jiska ek agreed meaning ho.

Kaun se field ki position freeze hoti hai, aur kyun

Opcode, taaki decode hamesha "kya kaam" pehle dhundh sake chicken-and-egg problem ke bina.

funct3 aur funct7 kya karte hain

Ek shared opcode family ke andar exact operation sub-select karte hain (jaise add ko sub se tell karna).

Register field ek storage box ko name karne wala number hold karta hai; immediate constant value khud hold karta hai.

Two's complement mein top bit kaun sa weight carry karta hai

- 2^{b - 1}

(negative), jabki saare lower bits

+ 2^{i}

rakhte hain.

12-bit two's-complement immediate ki range kya hai

- 2048

+ 2047

, yaani

- 2^{11}

2^{11} - 1

Sign extension top bit kyun copy karta hai zeros pad karne ki jagah

Negative numbers ko negative rakhne ke liye; zero-padding unhe bade positives mein badal deta.