Every read from or write to a storage device requires answering a fundamental question: where? The operating system must specify exactly which location on the disk contains the desired data or should receive new data. This location specification is disk addressing.

Over the decades, disk addressing has evolved from explicit physical coordinates to fully abstracted logical numbering. This evolution reflects the growing complexity of storage devices and the need for portable, scalable, and device-independent storage interfaces.

This page provides an exhaustive examination of the two primary addressing schemes—CHS (Cylinder-Head-Sector) and LBA (Logical Block Addressing)—their structure, limitations, translation mechanisms, and ongoing relevance in modern systems.

Cylinder-Head-Sector (CHS) addressing was the original method for specifying disk locations, directly mapping to the physical geometry of the drive. Understanding CHS is essential for interpreting legacy systems, boot sectors, and partition table structures.

1.1 CHS Address Components

A CHS address is a three-tuple (C, H, S):

Key Quirk: Sector numbers start at 1, not 0. This historical anomaly affects all CHS calculations.

1.2 CHS Address Encoding

In BIOS interrupt 13h (INT 13h), CHS addresses are encoded in registers as follows:

CH register:     Lower 8 bits of cylinder number
CL register:     Bits 7-6: Upper 2 bits of cylinder (10-bit total)
                 Bits 5-0: Sector number (6 bits, values 1-63)
DH register:     Head number (8 bits, values 0-255)

This encoding limits:

• Cylinders: 10 bits → 0-1023 (1024 total)
• Heads: 8 bits → 0-255 (256 total)
• Sectors: 6 bits → 1-63 (63 total)

1.3 Calculating CHS Capacity

The maximum addressable capacity with CHS:

$$\text{Max Sectors} = C \times H \times S = 1024 \times 256 \times 63 = 16,515,072 \text{ sectors}$$

$$\text{Max Capacity} = 16,515,072 \times 512 \text{ bytes} = 8,455,716,864 \text{ bytes} \approx 7.88 \text{ GiB} \approx 8.46 \text{ GB}$$

This is the famous 8.4 GB barrier (or 7.88 GiB) that plagued PC systems in the late 1990s.

Practical BIOS Limits:

Actual limits were often more restrictive due to BIOS implementations:

As drives exceeded BIOS CHS limits, intermediate solutions emerged to stretch the addressing space. These translation modes allowed larger drives while maintaining CHS compatibility.

2.1 Translation Concepts

Translation works by presenting a logical geometry to the operating system that differs from the physical geometry of the drive:

OS sees: Logical CHS (translated)
    ↓
BIOS translates
    ↓
Drive sees: Physical CHS or LBA

2.2 Common Translation Modes

2.3 Large (ECHS) Translation Details

The Large/ECHS mode works by manipulating the reported geometry:

Example:

• Physical geometry: 4,092 cylinders × 16 heads × 63 sectors
• This exceeds BIOS 1024 cylinder limit

Translation:

• Divide cylinders by 4: 4,092 ÷ 4 = 1,023 cylinders
• Multiply heads by 4: 16 × 4 = 64 heads
• Sectors unchanged: 63

Result:

• Logical geometry: 1,023 cylinders × 64 heads × 63 sectors
• Same total capacity, but within BIOS cylinder limit

Conversion Algorithm:

$$\text{Logical Cylinder} = \text{Physical Cylinder} \div 2^n$$ $$\text{Logical Head} = (\text{Physical Head} \times 2^n) + (\text{Physical Cylinder} \mod 2^n)$$

Where $n$ is chosen such that logical cylinders ≤ 1024.

2.4 LBA Translation Mode

In LBA translation mode, the BIOS:

1. Receives CHS address from OS
2. Converts CHS → LBA using reported logical geometry
3. Issues LBA command to drive
4. Drive's firmware maps LBA to physical location

This added a layer of abstraction but remained limited by the BIOS's 8.4 GB addressable space.

Logical Block Addressing (LBA) revolutionized disk addressing by abstracting away physical geometry entirely. Instead of specifying cylinder, head, and sector, LBA uses a simple linear numbering scheme.

3.1 LBA Fundamentals

Concept:

• View the disk as a linear array of blocks (sectors)
• Each block has a unique number: 0, 1, 2, ..., (Total Sectors - 1)
• No knowledge of physical geometry required

Example:

LBA 0 → First sector on the disk (typically MBR/GPT)
LBA 1 → Second sector
...
LBA 2,000,000,000 → Somewhere deep in a 1 TB drive

3.2 LBA Advantages

3.3 LBA Bit Width Evolution

3.4 INT 13h Extensions (EDD)

To address drives larger than 8.4 GB while maintaining BIOS compatibility, INT 13h Extensions (Enhanced Disk Drive, EDD) were developed:

Extended Read (INT 13h, AH=42h):

struct Disk_Address_Packet {
    uint8_t  packet_size;      /* Size of this packet (16 or greater) */
    uint8_t  reserved;         /* Zero */
    uint16_t sector_count;     /* Number of sectors to transfer */
    uint16_t buffer_offset;    /* Buffer offset (real mode) */
    uint16_t buffer_segment;   /* Buffer segment (real mode) */
    uint64_t start_lba;        /* Starting LBA (64-bit) */
};

This allows direct LBA addressing in BIOS code, bypassing CHS entirely.

Modern drives present LBA to the host but must internally translate to physical locations. This translation is more complex than a simple formula due to zone bit recording, defect management, and performance optimization.

4.1 Zone Mapping

With Zone Bit Recording (ZBR), tracks have varying sectors-per-track. The drive maintains a zone table:

Given an LBA, the firmware:

1. Searches the zone table to find which zone contains the LBA
2. Calculates the offset within the zone
3. Determines the physical cylinder, head, and sector

4.2 Defect Management

No magnetic surface is perfect. Defects are managed via:

P-List (Primary Defect List):

• Defects found during manufacturing
• Written to reserved area during factory testing
• Permanent; never changes

G-List (Growth Defect List):

• Defects discovered during drive operation
• Sectors that develop errors beyond ECC recovery
• Updated throughout drive lifetime

Defect Remapping:

When a defect is discovered:

1. The bad sector's LBA is noted
2. A spare sector (from reserved pool) is allocated
3. The translation table is updated: LBA → new physical location
4. Host continues using the same LBA; change is transparent

Spare Area Allocation:

Drives reserve capacity for spares:

• Typically 100-200 spare sectors per zone
• Additional spares at end of drive
• When spares exhaust, the drive reports imminent failure via SMART

4.3 Translation Table Structure

Modern drives use multi-level translation:

LBA → Zone Lookup → In-Zone Offset → Physical CHS → Defect Remap → Final Physical CHS

Performance Considerations:

• Translation tables are cached in drive's RAM
• Frequently accessed regions may have optimized lookup paths
• Table updates (defect remapping) are journaled to survive power loss

The Master Boot Record (MBR) partition table, designed in 1983, uses CHS addressing—creating fundamental limitations that still affect systems today.

5.1 MBR Partition Entry Structure

Each MBR partition entry (16 bytes) contains:

5.2 CHS Fields in MBR

The 3-byte CHS fields encode:

Byte 0: Head number (8 bits, 0-255)
Byte 1: Sector in bits 5-0 (6 bits, 1-63)
        Upper 2 bits of cylinder in bits 7-6
Byte 2: Lower 8 bits of cylinder

This limits CHS to 1024 cylinders × 256 heads × 63 sectors = 8.4 GB.

5.3 The Dual-Addressing Approach

MBR contains both CHS and LBA fields for each partition. Modern systems use LBA exclusively:

• LBA Start (4 bytes): 32-bit LBA of first sector
• Sector Count (4 bytes): 32-bit count of sectors

32-bit LBA Limit:

$$\text{Max Sectors} = 2^{32} - 1 = 4,294,967,295$$ $$\text{Max Capacity} = 4,294,967,295 \times 512 = 2,199,023,255,040 \text{ bytes} \approx 2 \text{ TiB}$$

This is the 2 TiB barrier for MBR partitioning.

5.4 CHS Values in Modern MBR

For drives larger than 8.4 GB, CHS fields use placeholder values:

• Start CHS: Often (0, 1, 1) for first partition or (254, 255, 255) for "beyond CHS limits"
• End CHS: (254, 255, 255) or (1023, 255, 63) indicating "max CHS"

Systems ignore CHS and use LBA fields instead.

The GUID Partition Table (GPT), part of the UEFI specification, eliminates CHS entirely and uses 64-bit LBA addressing for vast capacity support.

6.1 GPT Structure Overview

LBA 0:      Protective MBR (for legacy compatibility)
LBA 1:      Primary GPT Header
LBA 2-33:   Primary Partition Entries (128 entries × 128 bytes)
LBA 34-...: Usable Data Space
LBA -33...: Secondary Partition Entries (backup)
LBA -1:     Secondary GPT Header (backup)

6.2 GPT Partition Entry Structure

Each GPT partition entry is 128 bytes (expandable):

6.3 64-bit LBA Capacity

With 64-bit LBA addressing:

$$\text{Max Sectors} = 2^{64} - 1 \approx 1.84 \times 10^{19}$$ $$\text{Max Capacity (512B)} = 2^{64} \times 512 = 9.44 \times 10^{21} \text{ bytes} = 9.44 \text{ ZB}$$ $$\text{Max Capacity (4KB)} = 2^{64} \times 4096 = 7.55 \times 10^{22} \text{ bytes} = 75.5 \text{ ZB}$$

This capacity exceeds any foreseeable storage technology by many orders of magnitude.

6.4 Protective MBR

GPT includes a Protective MBR at LBA 0:

• Single partition entry spanning entire disk
• Type 0xEE ("GPT Protective")
• Prevents MBR-only tools from misidentifying the disk as unformatted
• Old tools see a "full disk" and won't offer to partition

6.5 GPT vs. MBR Addressing Comparison

Understanding how to examine and work with disk addresses is essential for troubleshooting, forensics, and low-level storage management. Here are practical tools and techniques.

7.1 Linux Tools

7.2 Windows Tools

We have traced the evolution of disk addressing from physical coordinates to logical abstraction. Let's consolidate the key concepts:

What's Next:

With addressing schemes understood, we complete our disk structure exploration with Disk Geometry—examining how physical and logical geometry relate, the translation mechanisms that bridge them, and how operating systems discover and work with drive geometry.