Quaternary (base 4)
Quaternary is the base-4 number system, using the digits 0 to 3.
Convert quaternary to any number system
3333 quaternary = 11111111 binary
Quick facts
- System
- Quaternary
- Base (radix)
- 4
- Digits
0 1 2 3- Notes
- Four digits, 0 to 3.
- Also called
- base 4
- Example
3333= 255 in decimal
3333 in other systems
| Binary | 11111111 |
| Decimal | 255 |
| Roman numerals | CCLV |
| Hexadecimal | FF |
| Octal | 377 |
| Duodecimal | 193 |
| Ternary | 100110 |
| Base 36 | 73 |
How quaternary works
Quaternary is the base-4 number system, using the digits 0 to 3. Each quaternary digit is exactly two bits. DNA, with its four bases A, C, G and T, is naturally a quaternary code.
Each position is worth 4 times the position to its right: 1, 4, 16, 64, 256 and so on. So 3333 means 3 × 43 + 3 × 42 + 3 × 41 + 3 × 40 = 255.
Where quaternary is used
- Encoding DNA sequences.
- Two-bit groupings in computing.
Quaternary chart
| Quaternary | Binary | Decimal | Roman numerals | Hexadecimal |
|---|---|---|---|---|
0 |
0 | 0 | – | 0 |
1 |
1 | 1 | I | 1 |
2 |
10 | 2 | II | 2 |
3 |
11 | 3 | III | 3 |
10 |
100 | 4 | IV | 4 |
11 |
101 | 5 | V | 5 |
12 |
110 | 6 | VI | 6 |
13 |
111 | 7 | VII | 7 |
20 |
1000 | 8 | VIII | 8 |
21 |
1001 | 9 | IX | 9 |
22 |
1010 | 10 | X | A |
23 |
1011 | 11 | XI | B |
30 |
1100 | 12 | XII | C |
31 |
1101 | 13 | XIII | D |
32 |
1110 | 14 | XIV | E |
33 |
1111 | 15 | XV | F |
100 |
10000 | 16 | XVI | 10 |
101 |
10001 | 17 | XVII | 11 |
102 |
10010 | 18 | XVIII | 12 |
103 |
10011 | 19 | XIX | 13 |
110 |
10100 | 20 | XX | 14 |
200 |
100000 | 32 | XXXII | 20 |
302 |
110010 | 50 | L | 32 |
1000 |
1000000 | 64 | LXIV | 40 |
1210 |
1100100 | 100 | C | 64 |
2000 |
10000000 | 128 | CXXVIII | 80 |
3333 |
11111111 | 255 | CCLV | FF |
10000 |
100000000 | 256 | CCLVI | 100 |
13310 |
111110100 | 500 | D | 1F4 |
33220 |
1111101000 | 1000 | M | 3E8 |
100000 |
10000000000 | 1024 | MXXIV | 400 |
Convert quaternary to…
Convert to quaternary
Numbers in quaternary
- 0
- 1
- 2
- 3
- 10
- 11
- 12
- 13
- 20
- 21
- 22
- 23
- 30
- 31
- 32
- 33
- 100
- 101
- 102
- 103
- 110
- 111
- 112
- 113
- 120
- 121
- 122
- 123
- 130
- 131
- 132
- 133
- 200
- 201
- 202
- 203
- 210
- 211
- 212
- 213
- 220
- 221
- 222
- 223
- 230
- 231
- 232
- 233
- 300
- 301
- 302
- 303
- 310
- 311
- 312
- 313
- 320
- 321
- 322
- 323
- 330
- 331
- 332
- 333
- 1000
- 1001
- 1002
- 1003
- 1010
- 1011
- 1012
- 1013
- 1020
- 1021
- 1022
- 1023
- 1030
- 1031
- 1032
- 1033
- 1100
- 1101
- 1102
- 1103
- 1110
- 1111
- 1112
- 1113
- 1120
- 1121
- 1122
- 1123
- 1130
- 1131
- 1132
- 1133
- 1200
- 1201
- 1202
- 1203
- 1210
Frequently asked questions
What is quaternary?
Quaternary is the base-4 number system, using the digits 0 to 3.
Which symbols does quaternary use?
Four digits, 0 to 3.
How do you write 10 in quaternary?
10 in quaternary is 22.
How do you write 100 in quaternary?
100 in quaternary is 1210.