# Interfacing ternary and binary components

A project log for Homebrew ternary computer

TRIADOR: The only ternary computer made for real in the past 50 years.

Ok, now it is kind of proven that binary CPLD (or FPGA) may implement ternary logic, but how we can integrate it with "true" ternary components, especially when CPLD is 3.3V and TRIMUXes are -5V and +5V? Answer is DG403 chips may do the job:

Because simplified ternary mutexes e12 and e21 can be easily implemented by DG403 integrated circuits:

```;Format of the triad:
;|7|6|5|4|3|2|1|0|
;|+|-|+|-|+|-|+|-|
;|par|low|mid|high
;par (parity) is not yet used, so it's always 0 0 for now...

tOOO    EQU    0x00 ; 0
tNOO    EQU    0x01 ; -9
tPOO    EQU    0x02 ; +9
tONO    EQU    0x04 ; -3
tNNO    EQU    0x05 ; -12
tPNO    EQU    0x06 ; +6
tOPO    EQU    0x08 ; +3
tNPO    EQU    0x09 ; -6
tPPO    EQU    0x0A ; +12
tOON    EQU    0x10 ; -1
tNON    EQU    0x11 ; -10
tPON    EQU    0x12 ; +8
tONN    EQU    0x14 ; -4
tNNN    EQU    0x15 ; -13
tPNN    EQU    0x16 ; +5
tOPN    EQU    0x18 ; +2
tNPN    EQU    0x19 ; -7
tPPN    EQU    0x1A ; +11
tOOP    EQU    0x20 ; +1
tNOP    EQU    0x21 ; -8
tPOP    EQU    0x22 ; +10
tONP    EQU    0x24 ; -2
tNNP    EQU    0x25 ; -11
tPNP    EQU    0x26 ; +7
tOPP    EQU    0x28 ; +4
tNPP    EQU    0x29 ; -5
tPPP    EQU    0x2A ; +13
```

As you can see we directly translate triad to byte and vice versa for data, but we can do the same for address - lower 3 trit of address can address the same 48 bytes (so instead of 27 triad one page will occupy 48 bytes of binary memory). Higher trits of address may or may not have similar translation.

Also we can have a special CPLD that converts ternary address to binary address optimally (without gaps and holes as above). Below you can see calculations for mostly used memory sizes:

2KB = 11-bit address = 6 trits (729 ternary cells - 28% used);

8KB = 13-bit address = 8 trits (6,561 ternary cells - 63% used);

32KB = 15-bit address = 9 trits (19,683 ternary cells - 48% used);

64KB = 16-bit address = 10 trits (59,049 ternary cells - 71% used);

128KB = 17-bit address = the same 10 trits (59,049 ternary cells - 45% used);

256KB = 18-bit address = 11 trits (177,147 ternary cells - 67% used);

512KB = 19-bit address = the same 11 trits (177,147 ternary cells - almost 34% used);

1MB = 20-bit address = 12 trits (531,441 ternary cells - almost 51% used).

As you can see we have better usage of binary memory in ternary computer system when it's 64KB addressed by 10 trits and this approach will use 71% of memory space.

In case of TRIADOR we have 6-trit address for program memory - it has addresses from -364 to +364 and each read-only memory cell should have 5-trit value - to simplify things in my Logisim model I addressed 2K binary ROM directly when every TRIT of ternary address is converted to 2 BITS of binary address, but in this case it has to be 12 bits total, but we have only 11 (2^11=2048) - my idea was to allow user to use ternary addresses from ONNNNN to PPPPPP only (it is 66% of all 6-trit address space and should be more than enough for start) and we need to convert 1-byte data to 5-trit program word by another smaller ROM (or CPLD):
```    <comp lib="4" loc="(850,300)" name="ROM">
<a name="dataWidth" val="10"/>
0 1 6 4 5 1a 18 19
12 10 11 16 14 15 6a 68
69 62 60 61 66 64 65 4a
48 49 42 40 41 46 44 45
5a 58 59 52 50 51 56 54
55 1aa 1a8 1a9 1a2 1a0 1a1 1a6
1a4 1a5 18a 188 189 182 180 181
186 184 185 19a 198 199 192 190
191 196 194 195 12a 128 129 122
120 121 126 124 125 10a 108 109
102 100 101 106 104 105 11a 118
119 112 110 111 116 114 115 16a
168 169 162 160 161 166 164 165
14a 148 149 142 140 141 146 144
145 15a 158 159 152 150 151 156
154 155 13*0 2aa 2a8 2a9 2a2 2a0
2a1 2a6 2a4 2a5 28a 288 289 282
280 281 286 284 285 29a 298 299
292 290 291 296 294 295 22a 228
229 222 220 221 226 224 225 20a
208 209 202 200 201 206 204 205
21a 218 219 212 210 211 216 214
215 26a 268 269 262 260 261 266
264 265 24a 248 249 242 240 241
246 244 245 25a 258 259 252 250
251 256 254 255 aa a8 a9 a2
a0 a1 a6 a4 a5 8a 88 89
82 80 81 86 84 85 9a 98
99 92 90 91 96 94 95 2a
28 29 22 20 21 26 24 25
a 8 9 2
</a>
</comp>
```

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