Minnesota State Community and Technical College

Moorhead, Minnesota

Number Conversion Helps


Decimal to Binary Example
Binary to Decimal Example
Hexadecimal to Binary Example
Binary to Hexadecimal Example
Decimal to Hexadecimal Example
Hexadecimal to Decimal Example
Decimal-Binary Conversion Chart
Binary, Decimal, and Hexadecimal Chart

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Decimal to Binary Example

This is one way to convert the decimal number 194 to binary.

Decimal	Binary	Original Number – Decimal	Binary Result
		194
128	1000 0000	194-128=66	1000 0000
64	0100 0000	66-64= 2	0100 0000
32	0010 0000	2-32=can't
16	0001 0000	2-16=can't
8	0000 1000	2-8=can't
4	0000 0100	2-4=can't
2	0000 0010	2-2=0	0000 0010
1	0000 0001	0-1=can't


Now, combine the binary numbers fro the Binary Result column. Make sure to maintain the same place value from the chart. In this case, decimal 194 is 1100 0010 in binary. The space in the middle (between nibbles) in binary is not necessary, but helps you see the relationship

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Binary to Decimal Example

This is one way to convert the binary number 10101010 to decimal.

Decimal	Binary	Original Binary Number	Decimal Numbers to Add
128	1000 0000	1000 0000	128
64	0100 0000
32	0010 0000	0010 0000	32
16	0001 0000
8	0000 1000	0000 1000	8
4	0000 0100
2	0000 0010	0000 0010	2
1	0000 0001


The original binary number is on the chart by place value. Performing an AND on the numbers will reproduce the original binary number. Once the place value is known in Decimal add the decimal numbers in the Decimal Numbers to Add for the decimal answer. 128 + 32 + 8 + 2 = 170

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Hexadecimal to Binary Example

This is one way to convert the hexadecimal number 5A to binary. This is a two step method. Convert each digit separately.

Hexadecimal	Nibble	10's place Binary	1's place Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101	0101
6	0110
7	0111
8	1000
9	1001
A	1010		1010
B	1011
C	1100
D	1101
E	1110
F	1111


In the number 5A, the number 5 is the most significant digit and A is the least significant digit. Another way of talking about 5A, the number 5 is in the 10's place value and A is in the 1's place value. The nibble for the most significant digit comes first in the binary number then the least significant digit. Therefore, the hexadecimal number 5A is 0101 1010 in binary.

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Binary to Hexadecimal Example

This is one way to convert the binary number 11001011 to hexadecimal. Divide the number into two nibbles. The most significant digits or the digits in the 10's place value are 1100. The least significant digits or the digits in the 1's place value are 1011.

Nibble 1	Hexadecimal	Hexadecimal Digit 1	Nibble 2	Hexadecimal	Hexadecimal Digit 2
0000	0		0000	0
0001	1		0001	1
0010	2		0010	2
0011	3		0011	3
0100	4		0100	4
0101	5		0101	5
0110	6		0110	6
0111	7		0111	7
1000	8		1000	8
1001	9		1001	9
1010	A		1010	A
1011	B		1011	B	B
1100	C	C	1100	C
1101	D		1101	D
1110	E		1110	E
1111	F		1111	F


Take the two matching hexadecimal digits and recombine them into the hexadecimal number. In this case, the binary number 11001011 is hexadecimal CB.

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Decimal to Hexadecimal Example

This one way to convert the decimal number 200 to hexadecimal. This is a two step method. First convert the decimal number to binary, then the binary number to hexadecimal.

Decimal	Binary	Original Number – Decimal	Binary Result
		200
128	1000 0000	200-128=72	1000 0000
64	0100 0000	72-64= 8	0100 0000
32	0010 0000	8-32=can't
16	0001 0000	8-16=can't
8	0000 1000	8-8=0	0000 1000
4	0000 0100	0-4=can't
2	0000 0010	0-2=can't
1	0000 0001	0-1=can't


The decimal number 200 is 11001000 in binary. Now convert 11001000 to hexadecimal. Divide 11001000 into nibbles. The most significant nibble or the nibble in the 10's place value is 1100. The least significant nibble or the nibble in the 1's place value is 1000.

Nibble 1	Hexadecimal	Hexadecimal Digit 1	Nibble 2	Hexadecimal	Hexadecimal Digit 2
0000	0		0000	0
0001	1		0001	1
0010	2		0010	2
0011	3		0011	3
0100	4		0100	4
0101	5		0101	5
0110	6		0110	6
0111	7		0111	7
1000	8		1000	8	8
1001	9		1001	9
1010	A		1010	A
1011	B		1011	B
1100	C	C	1100	C
1101	D		1101	D
1110	E		1110	E
1111	F		1111	F


Take the two matching hexadecimal digits and recombine them into the hexadecimal number. In this case, the binary 11001000 is hexadecimal C8.

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Hexadecimal to Decimal Example

This is one way to convert the hexadecimal number 59 to decimal. This is a two step process. First convert the hexadecimal number to binary. Then convert the binary number to decimal.

Nibble 1	Hexadecimal	Hexadecimal Digit 1	Nibble 2	Hexadecimal	Hexadecimal Digit 2
0000	0		0000	0
0001	1		0001	1
0010	2		0010	2
0011	3		0011	3
0100	4		0100	4
0101	5	5	0101	5
0110	6		0110	6
0111	7		0111	7
1000	8		1000	8
1001	9		1001	9	9
1010	A		1010	A
1011	B		1011	B
1100	C		1100	C
1101	D		1101	D
1110	E		1110	E
1111	F		1111	F


In the case of hexadecimal 59, the binary number is 01011001. Now convert binary 0101 1001 to decimal.

Decimal	Binary	Original Binary Number	Decimal Numbers to Add
128	1000 0000
64	0100 0000	0100 0000	64
32	0010 0000
16	0001 0000	0001 0000	16
8	0000 1000	0000 1000	8
4	0000 0100
2	0000 0010
1	0000 0001	0000 0001	1


The original binary number is on the chart by place value. Performing an AND on the numbers will reproduce the original binary number. Once the place value is known, add together the decimal numbers in the Decimal Numbers to Add column. 64 + 16 + 8 + 1 = 89. Therefore hexadecimal 59 is 89 decimal.

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Decimal-Binary Conversion Chart

The decimal and binary columns are useful when converting between decimal and binary. In test situations without a calculator, copy the decimal and binary columns usually helps. The space in the middle (between nibbles) in binary is not necessary, but helps you see the relationship.

Decimal	Binary	Decimal Exponent	Hexadecimal
128	1000 0000	2^7	80
64	0100 0000	2^6	40
32	0010 0000	2^5	20
16	0001 0000	2^4	10
8	0000 1000	2^3	8
4	0000 0100	2^2	4
2	0000 0010	2^1	2
1	0000 0001	2^0	1


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Binary, Decimal, and Hexadecimal Chart

This chart counts from 0 to 255 in decimal, binary, and hexadecimal. The space in the middle (between nibbles) in binary is not necessary, but helps you see a relationship.

Decimal	Binary	Hexadecimal
0	0000 0000	0
1	0000 0001	1
2	0000 0010	2
3	0000 0011	3
4	0000 0100	4
5	0000 0101	5
6	0000 0110	6
7	0000 0111	7
8	0000 1000	8
9	0000 1001	9
10	0000 1010	A
11	0000 1011	B
12	0000 1100	C
13	0000 1101	D
14	0000 1110	E
15	0000 1111	F
16	0001 0000	10
17	0001 0001	11
18	0001 0010	12
19	0001 0011	13
20	0001 0100	14
21	0001 0101	15
22	0001 0110	16
23	0001 0111	17
24	0001 1000	18
25	0001 1001	19
26	0001 1010	1A
27	0001 1011	1B
28	0001 1100	1C
29	0001 1101	1D
30	0001 1110	1E
31	0001 1111	1F
32	0010 0000	20
33	0010 0001	21
34	0010 0010	22
35	0010 0011	23
36	0010 0100	24
37	0010 0101	25
38	0010 0110	26
39	0010 0111	27
40	0010 1000	28
41	0010 1001	29
42	0010 1010	2A
43	0010 1011	2B
44	0010 1100	2C
45	0010 1101	2D
46	0010 1110	2E
47	0010 1111	2F
48	0011 0000	30
49	0011 0001	31
50	0011 0010	32
51	0011 0011	33
52	0011 0100	34
53	0011 0101	35
54	0011 0110	36
55	0011 0111	37
56	0011 1000	38
57	0011 1001	39
58	0011 1010	3A
59	0011 1011	3B
60	0011 1100	3C
61	0011 1101	3D
62	0011 1110	3E
63	0011 1111	3F
64	0100 0000	40
65	0100 0001	41
66	0100 0010	42
67	0100 0011	43
68	0100 0100	44
69	0100 0101	45
70	0100 0110	46
71	0100 0111	47
72	0100 1000	48
73	0100 1001	49
74	0100 1010	4A
75	0100 1011	4B
76	0100 1100	4C
77	0100 1101	4D
78	0100 1110	4E
79	0100 1111	4F
80	0101 0000	50
81	0101 0001	51
82	0101 0010	52
83	0101 0011	53
84	0101 0100	54
85	0101 0101	55
86	0101 0110	56
87	0101 0111	57
88	0101 1000	58
89	0101 1001	59
90	0101 1010	5A
91	0101 1011	5B
92	0101 1100	5C
93	0101 1101	5D
94	0101 1110	5E
95	0101 1111	5F
96	0110 0000	60
97	0110 0001	61
98	0110 0010	62
99	0110 0011	63
100	0110 0100	64
101	0110 0101	65
102	0110 0110	66
103	0110 0111	67
104	0110 1000	68
105	0110 1001	69
106	0110 1010	6A
107	0110 1011	6B
108	0110 1100	6C
109	0110 1101	6D
110	0110 1110	6E
111	0110 1111	6F
112	0111 0000	70
113	0111 0001	71
114	0111 0010	72
115	0111 0011	73
116	0111 0100	74
117	0111 0101	75
118	0111 0110	76
119	0111 0111	77
120	0111 1000	78
121	0111 1001	79
122	0111 1010	7A
123	0111 1011	7B
124	0111 1100	7C
125	0111 1101	7D
126	0111 1110	7E
127	0111 1111	7F
128	1000 0000	80
129	1000 0001	81
130	1000 0010	82
131	1000 0011	83
132	1000 0100	84
133	1000 0101	85
134	1000 0110	86
135	1000 0111	87
136	1000 1000	88
137	1000 1001	89
138	1000 1010	8A
139	1000 1011	8B
140	1000 1100	8C
141	1000 1101	8D
142	1000 1110	8E
143	1000 1111	8F
144	1001 0000	90
145	1001 0001	91
146	1001 0010	92
147	1001 0011	93
148	1001 0100	94
149	1001 0101	95
150	1001 0110	96
151	1001 0111	97
152	1001 1000	98
153	1001 1001	99
154	1001 1010	9A
155	1001 1011	9B
156	1001 1100	9C
157	1001 1101	9D
158	1001 1110	9E
159	1001 1111	9F
160	1010 0000	A0
161	1010 0001	A1
162	1010 0010	A2
163	1010 0011	A3
164	1010 0100	A4
165	1010 0101	A5
166	1010 0110	A6
167	1010 0111	A7
168	1010 1000	A8
169	1010 1001	A9
170	1010 1010	AA
171	1010 1011	AB
172	1010 1100	AC
173	1010 1101	AD
174	1010 1110	AE
175	1010 1111	AF
176	1011 0000	B0
177	1011 0001	B1
178	1011 0010	B2
179	1011 0011	B3
180	1011 0100	B4
181	1011 0101	B5
182	1011 0110	B6
183	1011 0111	B7
184	1011 1000	B8
185	1011 1001	B9
186	1011 1010	BA
187	1011 1011	BB
188	1011 1100	BC
189	1011 1101	BD
190	1011 1110	BE
191	1011 1111	BF
192	1100 0000	C0
193	1100 0001	C1
194	1100 0010	C2
195	1100 0011	C3
196	1100 0100	C4
197	1100 0101	C5
198	1100 0110	C6
199	1100 0111	C7
200	1100 1000	C8
201	1100 1001	C9
202	1100 1010	CA
203	1100 1011	CB
204	1100 1100	CC
205	1100 1101	CD
206	1100 1110	CE
207	1100 1111	CF
208	1101 0000	D0
209	1101 0001	D1
210	1101 0010	D2
211	1101 0011	D3
212	1101 0100	D4
213	1101 0101	D5
214	1101 0110	D6
215	1101 0111	D7
216	1101 1000	D8
217	1101 1001	D9
218	1101 1010	DA
219	1101 1011	DB
220	1101 1100	DC
221	1101 1101	DD
222	1101 1110	DE
223	1101 1111	DF
224	1110 0000	E0
225	1110 0001	E1
226	1110 0010	E2
227	1110 0011	E3
228	1110 0100	E4
229	1110 0101	E5
230	1110 0110	E6
231	1110 0111	E7
232	1110 1000	E8
233	1110 1001	E9
234	1110 1010	EA
235	1110 1011	EB
236	1110 1100	EC
237	1110 1101	ED
238	1110 1110	EE
239	1110 1111	EF
240	1111 0000	F0
241	1111 0001	F1
242	1111 0010	F2
243	1111 0011	F3
244	1111 0100	F4
245	1111 0101	F5
246	1111 0110	F6
247	1111 0111	F7
248	1111 1000	F8
249	1111 1001	F9
250	1111 1010	FA
251	1111 1011	FB
252	1111 1100	FC
253	1111 1101	FD
254	1111 1110	FE
255	1111 1111	FF


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Page Creation: 9/10/2003
Page Update: August 19, 2011