x86-64 Registers — Complete Technical Guide with REX Extension

x86-64 architecture extends the original x86 CPU register set from 8 to 16 general-purpose registers while maintaining full backward compatibility. This is achieved using a mechanism called the REX prefix, which adds one additional bit to existing 3-bit register fields.

1. CPU Registers Overview

Registers are the fastest storage units inside the CPU. They are used for:

• Arithmetic and logical operations

• Function calls and return values

• Memory addressing

• Loop control

• System-level execution

In x86-64, registers are 64-bit wide, but can also be accessed in smaller forms:

2. Original x86 Register Limitation

In the original x86 architecture:

• Registers were encoded using 3 bits

• This allowed only 8 registers

Mathematical limit:

$2^3 = 8$

Legacy x86 Registers (8 registers)

3. Why x86-64 Needed Expansion

Modern software requires:

• More function arguments

• More temporary registers for optimization

• Reduced memory access overhead

Thus, AMD introduced 8 additional registers:

• R8 to R15

However, the instruction encoding format could not be changed for backward compatibility.

4. REX Prefix Solution

The REX prefix is a single byte added before the opcode:

0100WRXB

It is always in the range:

xxxxxxxxxx
0x40 to 0x4F

REX Bit Meaning

5. Core Mechanism of Extension

x86 uses a 3-bit register field. REX adds one additional bit.

Thus, registers become 4-bit values:

$\text{Register ID} = (\text{REX bit} \ll 3) + \text{3-bit field}$

6. Full x86-64 Register Table

Complete Mapping of 16 Registers

7. How REX Computes Registers

Example: R10

• REX = 1

• 3-bit = 010

$(1 \ll 3) + 2 = 10$

Result: R10

Example: R13

• REX = 1

• 3-bit = 101

$(1 \ll 3) + 5 = 13$

Result: R13

8. Where REX Applies

REX extends multiple instruction fields:

9. Real Machine Code Example

Instruction:

xxxxxxxxxx
mov r10, rax

Machine code:

xxxxxxxxxx
4C 89 D0

Step 1: Decode REX (4C)

Binary:

xxxxxxxxxx
01001100

Breakdown:

• W = 1 → 64-bit operation

• R = 1 → REG extended

• X = 0

• B = 0

Step 2: Decode ModR/M (D0)

Binary:

xxxxxxxxxx
11010000

Split:

• REG = 010

• R/M = 000

Step 3: Apply REX Extension

• REG becomes R10

• R/M remains RAX

Final Instruction:

xxxxxxxxxx
mov r10, rax

10. Functional Role of Registers

RAX

• Arithmetic operations

• Function return values

RCX

• Loop counter

• Shift operations

RDX

• Multiplication/division support

RBX

• General-purpose storage

RSP

• Stack pointer (critical system register)

RBP

• Stack frame base pointer

RSI / RDI

• String and memory operations

R8–R15

• Function arguments and compiler temporary registers

11. Calling Convention (System V ABI)

12. Key Insight

The REX system does not change the original x86 encoding. It only adds one extra bit:

• Old registers: 000–111 (RAX–RDI)

• Extended registers: 1000–1111 (R8–R15)

13. Final Mental Model

x86-64 register encoding can be understood as:

• Original 3-bit field defines base register

• REX adds the missing most significant bit

So:

• 0xxx = legacy registers

• 1xxx = extended registers

Conclusion

x86-64 achieves register expansion without breaking compatibility by using a simple but powerful idea: a single prefix byte (REX) that extends existing 3-bit register fields into 4-bit addressing space, enabling 16 general-purpose registers while preserving the entire legacy x86 ecosystem.