Address range

Also called: address block, block of addresses, last address, first and last address, end address

The span of addresses from a first to a last address, inclusive. A block of N words starting at S ends at S + N − 1, and S to E holds E − S + 1 words.

An address range is a run of consecutive addresses, written first–last, such as 4000₁₆–7FFF₁₆. Both ends are included.

Two formulas do almost all the work:

Size of a range: from S to E there are E − S + 1 words.
End of a block: N words starting at S end at S + N − 1.

Both contain the same off-by-one: the +1 or −1 accounts for counting the first address. (Fence posts 3 to 5 are three posts, not two.) See off by one error.

Tricks that make hex ranges easy:

A whole memory (or a block starting at 0) ends at all 1s: a 2K memory ends at 7FF₁₆, a 64K one at FFFF₁₆.
Add 1 to an end address finishing in F digits and you get a round number, which makes subtraction easy: 3FFF₁₆ + 1 = 4000₁₆.
Sizes in hex: 1K = 400₁₆, 2K = 800₁₆, 4K = 1000₁₆, 8K = 2000₁₆, 16K = 4000₁₆, 32K = 8000₁₆.

Ranges are the building blocks of a memory map.

16³

16²

16¹

16⁰

Worked examples

Example

Where does a 4K block end?

A 4K block starts at 5000₁₆.

1.
4K = 4096 = 1000₁₆, so size − 1 = FFF₁₆.
2.
Last address = 5000₁₆ + FFF₁₆ = 5FFF₁₆ (the diagram).
3.
Check: the next block would start at 5FFF₁₆ + 1 = 6000₁₆ = 5000₁₆ + 1000₁₆. ✓

Example

How many words in a range?

Range 2C00₁₆ to 2FFF₁₆, inclusive.

1.
2FFF₁₆ − 2C00₁₆ = 3FF₁₆.
2.
Add 1: 400₁₆ = 1024 words = 1K.
3.
Quicker: the range ends just before 3000₁₆, so it holds 3000₁₆ − 2C00₁₆ = 400₁₆ words.

Common mistakes

Forgetting the +1. 2000₁₆ to 2FFF₁₆ is 1000₁₆ words, not FFF₁₆.
Ending a block at start + size. That's the first address of the next block.
Doing the subtraction in decimal digits. Hex borrows in 16s; convert or count carefully.

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