The Byte That Makes a ROM Add Up to Zero

The VIC-20 on my bench still won’t boot, and last night I talked myself into blaming the character ROM. So I pulled it, dropped it in the reader, and dumped 4 KB of hex. Then came the question every restorer eventually hits: is this the right four kilobytes, or did a flaky pin on a forty-year-old chip hand me garbage that only looks like data?

The answer these machines shipped with is almost insultingly plain. Add every byte together, throw away the carry above 255, and reserve one byte at the end to be whatever value drags that running total back to zero. Later, sum the whole thing again — if you don’t land on $00, something rotted.

package main

import "fmt"

func main() {
	data := []byte{0x20, 0x8B, 0xE3, 0x60} // four ROM bytes
	var sum byte
	for _, b := range data {
		sum += b // 8-bit accumulator, wraps at 256
	}
	check := -sum // the byte that drags the total back to zero
	fmt.Printf("check byte $%02X; verify total $%02X\n", check, sum+check)
}

The wrap is the whole game. An 8-bit accumulator doesn’t overflow into an error — it rolls over at 256, and the arithmetic is defined because of that, not in spite of it. The check byte is the two’s complement of the sum, so the grand total closes at zero. Verifying a good ROM is one loop and one comparison, cheap enough that a 1 MHz 6502 could run it at power-on and nobody would notice the delay.

local data = {0x20, 0x8B, 0xE3, 0x60}
local sum = 0
for _, b in ipairs(data) do
  sum = (sum + b) % 256   -- keep it inside one byte
end
local check = (256 - sum) % 256
print(string.format("check byte $%02X; verify total $%02X",
                    check, (sum + check) % 256))

Same idea, and that % 256 is doing by hand what Go’s byte type gets for free.

Both print check byte $12; verify total $00. It’s weak by modern standards — swap two bytes and the sum never flinches, which is why CRCs took over the moment cycles got cheap. But for catching a dead address line or a half-erased EPROM, a one-byte sum is honest work. When my next dump comes back and the total isn’t $00, I’ll at least know the chip is lying to me before I go blaming the power rail again.