Binary Memory Address Calculator
Calculate a final memory address from a base address and byte offset. Enter the starting address, offset and address width to view the resulting hexadecimal, decimal and binary memory address.
What Is a Memory Address?
A memory address is a numerical identifier for a location in an address space. Processors, microcontrollers, operating systems, debuggers and hardware peripherals use addresses to identify locations containing instructions, data, registers or mapped devices.
Addresses are commonly written in hexadecimal because hexadecimal maps compactly to binary. For example, hexadecimal 0x1000 represents decimal 4096 and binary 0001000000000000 when displayed as a 16-bit address.
How the Binary Memory Address Calculator Works
The calculator starts from a base memory address and adds a byte offset. The result is the final address of the target byte relative to the supplied base.
Offset: 32 bytes
32 decimal: 0x20
Final Address: 0x1000 + 0x20 = 0x1020
Memory Address Formula
The direct formula is:
Both values ultimately represent integers. The calculator accepts the base in hexadecimal because that is the notation commonly used for memory addresses, and accepts the offset in decimal bytes for convenience.
Memory Address Example
Suppose an embedded peripheral starts at address 0x4000 and a register is located 20 bytes from the beginning of that peripheral block.
Offset: 20 decimal = 0x14
Address: 0x4000 + 0x14 = 0x4014
The resulting register address is therefore 0x4014.
Base Address and Offset
A base address identifies the beginning of a memory region or object. An offset specifies a distance from that beginning.
Offset: Distance from base
Final Address: Base + Offset
Offsets are often used for structure fields, array elements, memory-mapped registers, file positions and hardware registers.
Hexadecimal Memory Addresses
Hexadecimal is common for memory addresses because one hexadecimal digit corresponds exactly to four binary bits.
| Hex Address | Decimal | 16-Bit Binary |
|---|---|---|
| 0x0000 | 0 | 0000000000000000 |
| 0x0010 | 16 | 0000000000010000 |
| 0x0100 | 256 | 0000000100000000 |
| 0x1000 | 4096 | 0001000000000000 |
| 0xFFFF | 65535 | 1111111111111111 |
Binary Memory Address Representation
Although addresses are usually displayed in hexadecimal, processors fundamentally operate with binary bit patterns. The calculator therefore displays the final address as a fixed-width binary value.
16-bit Binary: 0001000000100000
Leading zeros are preserved so the binary representation matches the selected address width.
16-Bit Memory Address Example
A 16-bit address contains sixteen address bits and can represent values from 0x0000 through 0xFFFF.
Hex: 0x0000 to 0xFFFF
If a calculation produces an address above 0xFFFF, it cannot fit within an unsigned 16-bit address space.
32-Bit Memory Address Example
An unsigned 32-bit address can represent values from 0 through 4,294,967,295.
Maximum: 0xFFFFFFFF
The selected address width on this calculator is used to validate the final numerical result and determine the number of binary and hexadecimal digits displayed.
Memory-Mapped Register Address Example
Hardware documentation frequently defines a peripheral base address and lists individual registers as offsets.
Register Offset: 32 bytes = 0x20
Register Address: 0x40020020
This is a common use of base-plus-offset addressing in embedded systems.
Array Element Address Example
If the base address of an array is known, an element can be located by adding the appropriate byte offset. The offset itself may first be calculated from element index and element size in software.
Calculated Byte Offset: 24
Element Address: 0x2018
This calculator handles the base-plus-byte-offset stage only. It does not calculate array indexing formulas automatically.
Memory Address Overflow
A computed address must fit inside the selected address width. For example, the maximum unsigned 16-bit address is 0xFFFF.
Offset: 32 = 0x20
Mathematical result: 0x10010
That result requires more than 16 bits, so this calculator reports an address-width overflow instead of silently wrapping around.
Why the Calculator Does Not Wrap Addresses
Some processors perform modular arithmetic when addresses overflow, but automatically wrapping an address could hide an error in a manual calculation.
This calculator therefore validates the result against the selected width and reports an error when the final address exceeds the maximum value.
Memory Addresses in Embedded Systems
Embedded systems frequently expose memory-mapped peripherals at fixed base addresses. Registers inside those peripherals are then identified by byte offsets.
Datasheets may show entries such as control register at offset 0x00, status register at 0x04 and data register at 0x08. Adding those offsets to the peripheral base yields the absolute register addresses.
Memory Addresses in Debugging
Debuggers, crash reports and memory viewers often display hexadecimal addresses. When a software structure or buffer begins at a known base location, calculating an address from an offset can help locate a field or byte during debugging.
The calculator provides decimal and binary equivalents as additional views of the same address value.
Memory Address vs Storage Alignment
The previous Binary Storage Alignment Calculator and this page answer different questions.
| Tool | Main Question |
|---|---|
| Binary Storage Alignment Calculator | How much padding is needed to align a data size? |
| Binary Memory Address Calculator | What address results from adding an offset to a base? |
Storage alignment deals primarily with data size and boundaries. Memory addressing deals with numerical locations inside an address space.
Memory Address vs Memory Map
A memory address identifies one location. A memory map describes how multiple regions occupy an entire address space.
Memory Map: Multiple regions with start and end addresses
For that reason, this tool does not attempt to construct or analyze multiple memory regions.
Memory Address vs Cache Address Breakdown
A cache-address calculation separates an address into fields such as tag, set index and block offset. That requires cache configuration parameters in addition to the address itself.
This calculator performs only the earlier base-plus-offset address calculation and leaves cache-specific decomposition to the dedicated cache tool.
Important Binary Memory Address Notes
The base address is entered in hexadecimal.
An optional 0x prefix is accepted.
The byte offset must be a non-negative whole number.
The calculator supports 8, 16, 24 and 32-bit unsigned address widths.
The base and final addresses must both fit inside the selected address width.
If the final address exceeds the selected width, the calculator reports overflow rather than wrapping around.
Binary output is padded with leading zeros to match the chosen address width.
This tool does not calculate alignment padding, cache tag/index fields, virtual-to-physical translation, array-index offsets or complete memory maps.
For real hardware, verify the address range, register offsets and addressing rules in the processor or peripheral documentation.