Find a pixel in Spectrum memory

A position such as x=14, y=64 is useful to a player. The drawing routine needs a memory address. We will connect the two, one byte at a time.

Coordinates start at zero inside the border: x=0 is the left edge and y=0 is the top. An X coordinate has two jobs. Dividing by eight selects the byte column; the remainder selects a bit within that byte. At x=14 the column is 1 and the remainder is 6.

Start with one visible bit

This complete program calls pixel_address with D=64 and E=14. D holds Y; E holds X. The routine returns the address in HL and preserves BC and DE. AF and HL change. Those promises are its contract.

It stores the returned address in the two-byte variable address, then writes %00000010 there. That is the bit for remainder 6: bit 7 corresponds to the leftmost pixel, so bit 1 is six places along.

The inspector should show 18433, hexadecimal $4801. The pixel is near the left edge, one-third down the picture area. An address can be correct even when a single pixel is difficult to spot.

Why Y is split into pieces

The Spectrum does not store bitmap rows in ordinary top-to-bottom order. Split the eight bits of Y into three groups:

The address also contains the fixed $4000 bitmap base. AND keeps the needed bits. Rotates put them in their destination positions; OR combines groups that occupy different bit positions. H receives the high address byte; L receives the low byte.

pixel_address:
 ld a,d
 and 7
 or $40
 ld h,a
 ld a,d
 and $C0
 rrca
 rrca
 rrca
 or h
 ld h,a
 ld a,d
 and $38
 rlca
 rlca
 ld l,a
 ld a,e
 rrca
 rrca
 rrca
 and 31
 or l
 ld l,a
 ret

At y=64, only Y bit 6 is set, contributing $0800. At x=14, the byte column contributes 1. The sum is $4000 + $0800 + 1 = $4801.

Check a boundary

Replace ld d,64 with ld d,65. Before assembling, predict $4901: we have changed the scanline within this character row, adding 256 to the address. Now try y=71 followed by y=72. Their addresses are $4F01 and $4821; the next visible row can have a smaller memory address.

Keep X between 0 and 255 and Y between 0 and 191 in this experiment. The routine does not reject off-screen coordinates; its caller owns that responsibility.