Format a Byte as Hexadecimal on Spectrum

Two hexadecimal digits are a compact way to show a byte in a debugger, password or diagnostic panel.

Use it in a project

VALUE is any byte. Return two ASCII codes, HIGH_CHAR then LOW_CHAR. LOWERCASE=0 selects A–F; any other value selects a–f. No terminator or display write is emitted.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: HIGH_CHAR, LOW_CHAR, VALUE, LOWERCASE. They occupy 4 contiguous bytes. Also reserve the private workspace: T0, T1, T2 (3 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call hexadecimal_format_init once at the intended reset boundary. It clears inputs as well as outputs and workspace. Set your starting state and configuration afterwards, then call hexadecimal_format_step whenever the described event occurs. The helper reads no device, waits for no frame and installs no interrupt handler.

Each nibble selects a decimal digit or a letter offset. The output order is most-significant nibble first, regardless of the machine’s word byte order.

Reusable initialisation and service

; SPDX-License-Identifier: MIT
; Format a Byte as Hexadecimal. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
hexadecimal_format_init:
    ld a,0
    ld (HIGH_CHAR),a
    ld (LOW_CHAR),a
    ld (VALUE),a
    ld (LOWERCASE),a
    ld (T0),a
    ld (T1),a
    ld (T2),a
    ret
hexadecimal_format_step:
; T0 = VALUE >> 4
    ld a,(VALUE)
    srl a
    srl a
    srl a
    srl a
    ld (T0),a
; T1 = VALUE & 15
    ld a,(VALUE)
    and 15
    ld (T1),a
; HIGH_CHAR = T0 + 48
    ld a,(T0)
    add a,48
    ld (HIGH_CHAR),a
; LOW_CHAR = T1 + 48
    ld a,(T1)
    add a,48
    ld (LOW_CHAR),a
; T2 = 55
    ld a,55
    ld (T2),a
; if LOWERCASE != 0:
    ld a,(LOWERCASE)
    cp 0
    jp nz,hexadecimal_format_L1
    jp hexadecimal_format_L2
hexadecimal_format_L1:
; T2 = 87
    ld a,87
    ld (T2),a
    jp hexadecimal_format_L3
hexadecimal_format_L2:
hexadecimal_format_L3:
; if T0 >= 10:
    ld a,(T0)
    cp 10
    jp nc,hexadecimal_format_L4
    jp hexadecimal_format_L5
hexadecimal_format_L4:
; HIGH_CHAR = T0 + T2
    ld a,(T0)
    ld b,a
    ld a,(T2)
    ld c,a
    ld a,b
    add a,c
    ld (HIGH_CHAR),a
    jp hexadecimal_format_L6
hexadecimal_format_L5:
hexadecimal_format_L6:
; if T1 >= 10:
    ld a,(T1)
    cp 10
    jp nc,hexadecimal_format_L7
    jp hexadecimal_format_L8
hexadecimal_format_L7:
; LOW_CHAR = T1 + T2
    ld a,(T1)
    ld b,a
    ld a,(T2)
    ld c,a
    ld a,b
    add a,c
    ld (LOW_CHAR),a
    jp hexadecimal_format_L9
hexadecimal_format_L8:
hexadecimal_format_L9:
    ret
component_end:

Machine contract

AF/BC/DE/HL may change; IX/IY are preserved. A direct CALL needs two return-address stack bytes. The helper makes no nested calls and adds no other stack use. Its named scratch is private workspace, not a pointer, a ROM variable or shared zero-page space that the game may borrow concurrently. The samples use fixed symbol bindings. Scope or rename every label and binding, including the component_end measurement marker, and allocate a separate block for each independent instance. Different helpers can also use common field names, so combining them needs separate namespaces or explicitly renamed bindings. Give each block one mutation owner.

The 48K diagnostic boots through ROM tape loading and USR, disables interrupts and owns the screen. The helper performs no port or screen writes.

Adapt the caller

demo.asm supplies the bindings and include order. exercise.inc first runs table cases, then a separate client retaining state between calls. A game can call the public step entry directly and remove the diagnostic packet and display. Do not copy the diagnostic’s hardware takeover into an existing game loop.

Build with make ASM198X=/path/to/asm198x. The Makefile produces normal, custom, deliberately wrong and repaired programs. Tools must already be installed; the sample downloads nothing.

Bindings and include order

    org $8000
CUSTOM equ 0
BROKEN equ 0
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
HIGH_CHAR: defb 0
LOW_CHAR: defb 0
VALUE: defb 0
LOWERCASE: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

A client retaining state between calls

preview_rules:
    if CUSTOM
; VALUE = 254
    ld a,254
    ld (VALUE),a
; LOWERCASE = 1
    ld a,1
    ld (LOWERCASE),a
    if BROKEN
; VALUE = VALUE & 15
    ld a,(VALUE)
    and 15
    ld (VALUE),a
    endif
    call checked_step
    call emit_state
    ret
    else
; VALUE = 171
    ld a,171
    ld (VALUE),a
    if BROKEN
; VALUE = VALUE & 15
    ld a,(VALUE)
    and 15
    ld (VALUE),a
    endif
    call checked_step
    call emit_state
    endif
    ret

Customise it

Select lower-case digits for FE. The maintained custom caller changes its inputs or client sequence rather than hiding a different implementation behind the same label. Compare every state of the two clients, not only their final display.

Custom client selection

    org $8000
CUSTOM equ 1
BROKEN equ 0
COYOTE_STEPS equ 2
BUFFER_STEPS equ 2
TEXT_CAP equ 4
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 49
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
HIGH_CHAR: defb 0
LOW_CHAR: defb 0
VALUE: defb 0
LOWERCASE: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

The custom diagnostic row is 66 65 FE 01 00 00 00 00. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller keeps only the low nibble. AB becomes 0B. Pass the whole byte and let the formatter split the two digits.

The BROKEN branch lives in the sequential client, not the reusable helper. wrong.asm selects it; repaired.asm restores the normal call sequence. The repaired executable matches the normal program (for Spectrum, compare loaded CODE rather than the tape filename).

Select the deliberately wrong client

    org $8000
CUSTOM equ 0
BROKEN equ 1
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
    include "caller.inc"
    include "exercise.inc"
component_start:
    include "component.inc"
    include "data.inc"
    include "cases.inc"
    include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
HIGH_CHAR: defb 0
LOW_CHAR: defb 0
VALUE: defb 0
LOWERCASE: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
    end start

Cost and alternatives

The measured helper extent is 141 code bytes; public state is 4 bytes and private scratch is 3 bytes. There are no immutable helper tables. Caller data, the test cases, return-address stack, alignment and display buffers cost additional space. These are assembled sizes, not cycle measurements.

Constant work with no lookup table. A sixteen-byte digit table saves branches at the cost of ROM space.

The output is ASCII, not PETSCII screen codes or a NES tile index. Translate through the game’s font mapping before drawing.

Execution evidence

Four variants run on 48K PAL ROM tape load and USR, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 64 boundary/varied/error table cases, dirty initialisation and the separate retained-state client. An independent mathematical/container model checks every public byte after every call. This is bounded example coverage, not exhaustive correctness for every possible state.

The records retain loaded immutable code, completion, register sentinels, full packets, source/tool/firmware hashes and captures. The public gate validates these retained observations and rejects altered evidence; it does not run restricted firmware. No firmware is distributed. The eight displayed bytes are the first eight public fields, zero-padded when shorter; the packet includes every field.

Where it fits

Decimal formatting: Hexadecimal needs two nibbles; decimal needs division into base-ten digits.

The Craft · Maths for Games · Source and native evidence.