mathschallenge.net logo

Frequently Asked Questions

What are binary and hexadecimal codes?

Many encryption systems will make use of binary and hexadecimal. This section provides a reference to help code breakers unfamiliar with these two systems.

The decimal number system, with which we are familiar, is based on counting in 10"s and makes use of ten digits: 0-9. For example,
3047 = 3×1000 + 0×100 + 4×10 + 7×1.

In a similar way, binary is based on counting in 2's and makes use of two digits: 0 and 1. For example,
110101=1×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 5310 (base 10).

Hexadecimal is based on counting in 16's, but in order to make use of 16 digits it uses 0-9 plus A (10), B (11), C (12), D (13), E (14) and F (15).
For example, 3D5 = 3×256 + 13×16 + 5×1 = 98110.

For reference, the following table lists the decimal/binary/hexadecimal equivalents of the numbers 1 through 255.


Decimal

Binary

Hexadecimal


Decimal

Binary

Hexadecimal
0
00000000
00
 
128
10000000
80
1
00000001
01
 
129
10000001
81
2
00000010
02
 
130
10000010
82
3
00000011
03
 
131
10000011
83
4
00000100
04
 
132
10000100
84
5
00000101
05
 
133
10000101
85
6
00000110
06
 
134
10000110
86
7
00000111
07
 
135
10000111
87
8
00001000
08
 
136
10001000
88
9
00001001
09
 
137
10001001
89
10
00001010
0A
 
138
10001010
8A
11
00001011
0B
 
139
10001011
8B
12
00001100
0C
 
140
10001100
8C
13
00001101
0D
 
141
10001101
8D
14
00001110
0E
 
142
10001110
8E
15
00001111
0F
 
143
10001111
8F
16
00010000
10
 
144
10010000
90
17
00010001
11
 
145
10010001
91
18
00010010
12
 
146
10010010
92
19
00010011
13
 
147
10010011
93
20
00010100
14
 
148
10010100
94
21
00010101
15
 
149
10010101
95
22
00010110
16
 
150
10010110
96
23
00010111
17
 
151
10010111
97
24
00011000
18
 
152
10011000
98
25
00011001
19
 
153
10011001
99
26
00011010
1A
 
154
10011010
9A
27
00011011
1B
 
155
10011011
9B
28
00011100
1C
 
156
10011100
9C
29
00011101
1D
 
157
10011101
9D
30
00011110
1E
 
158
10011110
9E
31
00011111
1F
 
159
10011111
9F
32
00100000
20
 
160
10100000
A0
33
00100001
21
 
161
10100001
A1
34
00100010
22
 
162
10100010
A2
35
00100011
23
 
163
10100011
A3
36
00100100
24
 
164
10100100
A4
37
00100101
25
 
165
10100101
A5
38
00100110
26
 
166
10100110
A6
39
00100111
27
 
167
10100111
A7
40
00101000
28
 
168
10101000
A8
41
00101001
29
 
169
10101001
A9
42
00101010
2A
 
170
10101010
AA
43
00101011
2B
 
171
10101011
AB
44
00101100
2C
 
172
10101100
AC
45
00101101
2D
 
173
10101101
AD
46
00101110
2E
 
174
10101110
AE
47
00101111
2F
 
175
10101111
AF
48
00110000
30
 
176
10110000
B0
49
00110001
31
 
177
10110001
B1
50
00110010
32
 
178
10110010
B2
51
00110011
33
 
179
10110011
B3
52
00110100
34
 
180
10110100
B4
53
00110101
35
 
181
10110101
B5
54
00110110
36
 
182
10110110
B6
55
00110111
37
 
183
10110111
B7
56
00111000
38
 
184
10111000
B8
57
00111001
39
 
185
10111001
B9
58
00111010
3A
 
186
10111010
BA
59
00111011
3B
 
187
10111011
BB
60
00111100
3C
 
188
10111100
BC
61
00111101
3D
 
189
10111101
BD
62
00111110
3E
 
190
10111110
BE
63
00111111
3F
 
191
10111111
BF
64
01000000
40
 
192
11000000
C0
65
01000001
41
 
193
11000001
C1
66
01000010
42
 
194
11000010
C2
67
01000011
43
 
195
11000011
C3
68
01000100
44
 
196
11000100
C4
69
01000101
45
 
197
11000101
C5
70
01000110
46
 
198
11000110
C6
71
01000111
47
 
199
11000111
C7
72
01001000
48
 
200
11001000
C8
73
01001001
49
 
201
11001001
C9
74
01001010
4A
 
202
11001010
CA
75
01001011
4B
 
203
11001011
CB
76
01001100
4C
 
204
11001100
CC
77
01001101
4D
 
205
11001101
CD
78
01001110
4E
 
206
11001110
CE
79
01001111
4F
 
207
11001111
CF
80
01010000
50
 
208
11010000
D0
81
01010001
51
 
209
11010001
D1
82
01010010
52
 
210
11010010
D2
83
01010011
53
 
211
11010011
D3
84
01010100
54
 
212
11010100
D4
85
01010101
55
 
213
11010101
D5
86
01010110
56
 
214
11010110
D6
87
01010111
57
 
215
11010111
D7
88
01011000
58
 
216
11011000
D8
89
01011001
59
 
217
11011001
D9
90
01011010
5A
 
218
11011010
DA
91
01011011
5B
 
219
11011011
DB
92
01011100
5C
 
220
11011100
DC
93
01011101
5D
 
221
11011101
DD
94
01011110
5E
 
222
11011110
DE
95
01011111
5F
 
223
11011111
DF
96
01100000
60
 
224
11100000
E0
97
01100001
61
 
225
11100001
E1
98
01100010
62
 
226
11100010
E2
99
01100011
63
 
227
11100011
E3
100
01100100
64
 
228
11100100
E4
101
01100101
65
 
229
11100101
E5
102
01100110
66
 
230
11100110
E6
103
01100111
67
 
231
11100111
E7
104
01101000
68
 
232
11101000
E8
105
01101001
69
 
233
11101001
E9
106
01101010
6A
 
234
11101010
EA
107
01101011
6B
 
235
11101011
EB
108
01101100
6C
 
236
11101100
EC
109
01101101
6D
 
237
11101101
ED
110
01101110
6E
 
238
11101110
EE
111
01101111
6F
 
239
11101111
EF
112
01110000
70
 
240
11110000
F0
113
01110001
71
 
241
11110001
F1
114
01110010
72
 
242
11110010
F2
115
01110011
73
 
243
11110011
F3
116
01110100
74
 
244
11110100
F4
117
01110101
75
 
245
11110101
F5
118
01110110
76
 
246
11110110
F6
119
01110111
77
 
247
11110111
F7
120
01111000
78
 
248
11111000
F8
121
01111001
79
 
249
11111001
F9
122
01111010
7A
 
250
11111010
FA
123
01111011
7B
 
251
11111011
FB
124
01111100
7C
 
252
11111100
FC
125
01111101
7D
 
253
11111101
FD
126
01111110
7E
 
254
11111110
FE
127
01111111
7F
 
255
11111111
FF