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You can create binary (base 2) numbers by adding exponents of 2, rather than exponents of 10 as in the decimal system. Binary numbers are used for basic computers because the 0 or 1 or 0 can be expressed as a switch, where 1 is on, and 0 is off.
Starting at the right you have 1's, as in decimals. Moving to the left, you have columns that double in value, rather than 10 times the value. The only values used are either 0 or 1.
For the number 111 in binary, the three ones are not one "hundred" plus one "ten" plus one "one"and eleven, but rather one (22 = 4), one (21 = 2) plus one (20 =1).
1 1 1 (binary) = 4 + 2 + 1 = 7
and
101 (binary) = 4 + 0 + 1 = 5
The column values for the first 8 digits are
128, 64, 32, 16, 8, 4, 2, 1
so the number 00011010 = 16 + 8 + 0 + 2 + 0 = 26
The first few numbers, arranged 4 bits (0's and 1's) to a "word":
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
16 = 0001 0000
17 = 0001 0001
18 = 0001 0010
19 = 0001 0011
20 = 0001 0100
21 = 0001 0101
22 = 0001 0110
23 = 0001 0111
24 = 0001 1000
100 would be 0110 0100
(0x128)+(1x64)+(1x32)+(0x16)+(0x8)+(1x4)+(0x2)+(0x1)
The binary units are 1, 2, 4, 8, 16, 32, 64, 128, and higher exponents of 2.
The integral binary numbers are expressed in terms of these units, the right side digit being a value of 0 or 1, the next digit a value of 0 or 2, the next a value of 0 or 4, and so forth.
0 = 0
1 = 1 (with any number of leading zeroes, e.g. 001= 00001 = 1)
2 = 10 (1 x 2 plus 0 x 1)
3 = 11 (1 x 2 plus 1 x 1)
4 = 100 (1 x 4 plus 0 x 2 plus 0 x 1)
5 = 101 (1 x 4 plus 0 x 2 plus 1 x 1)
Any binary number can be decoded by adding these unit values.
The first 8 columns of values are
128, 64, 32, 16, 8, 4, 2, 1
For example,
1100100 = 1 x 64, plus 1 x 32, plus 0 x 16, plus 0 x 8, plus 1 x 4, plus 0 x 2, plus 0 x 1
= 64 + 32 + 0 + 0 + 4 + 0 + 0
= 100
List of Numbers
The first 200 binary numbers expressed as 8 digits (with leading zeroes) are:
0 00000000
1 00000001
2 00000010
3 00000011
4 00000100
5 00000101
6 00000110
7 00000111
8 00001000
9 00001001
10 00001010
11 00001011
12 00001100
13 00001101
14 00001110
15 00001111
16 00010000
17 00010001
18 00010010
19 00010011
20 00010100
21 00010101
22 00010110
23 00010111
24 00011000
25 00011001
26 00011010
27 00011011
28 00011100
29 00011101
30 00011110
31 00011111
32 00100000
33 00100001
34 00100010
35 00100011
36 00100100
37 00100101
38 00100110
39 00100111
40 00101000
41 00101001
42 00101010
43 00101011
44 00101100
45 00101101
46 00101110
47 00101111
48 00110000
49 00110001
50 00110010
51 00110011
52 00110100
53 00110101
54 00110110
55 00110111
56 00111000
57 00111001
58 00111010
59 00111011
60 00111100
61 00111101
62 00111110
63 00111111
64 01000000
65 01000001
66 01000010
67 01000011
68 01000100
69 01000101
70 01000110
71 01000111
72 01001000
73 01001001
74 01001010
75 01001011
76 01001100
77 01001101
78 01001110
79 01001111
80 01010000
81 01010001
82 01010010
83 01010011
84 01010100
85 01010101
86 01010110
87 01010111
88 01011000
89 01011001
90 01011010
91 01011011
92 01011100
93 01011101
94 01011110
95 01011111
96 01100000
97 01100001
98 01100010
99 01100011
100 01100100
101 01100101
102 01100110
103 01100111
104 01101000
105 01101001
106 01101010
107 01101011
108 01101100
109 01101101
110 01101110
111 01101111
112 01110000
113 01110001
114 01110010
115 01110011
116 01110100
117 01110101
118 01110110
119 01110111
120 01111000
121 01111001
122 01111010
123 01111011
124 01111100
125 01111101
126 01111110
127 01111111
128 10000000
129 10000001
130 10000010
130 10000011
132 10000100
133 10000101
134 10000110
135 10000111
136 10001000
137 10001001
138 10001010
139 10001011
140 10001100
141 10001101
142 10001110
143 10001111
144 10010000
145 10010001
146 10010010
147 10010011
148 10010100
149 10010101
150 10010110
151 10010111
152 10011000
153 10011001
154 10011010
155 10011011
156 10011100
157 10011101
158 10011110
159 10011111
160 10100000
161 10100001
162 10100010
163 10100011
164 10100100
165 10100101
166 10100110
167 10100111
168 10101000
169 10101001
170 10101010
171 10101011
172 10101100
173 10101101
174 10101110
175 10101111
176 10110000
177 10110001
178 10110010
179 10110011
180 10110100
181 10110101
182 10110110
183 10110111
184 10111000
185 10111001
186 10111010
187 10111011
188 10111100
189 10111101
190 10111110
191 10111111
192 11000000
193 11000001
194 11000010
195 11000011
196 11000100
197 11000101
198 11000110
199 11000111
200 11001000
200 = 128 + 64 + (0x32) + (0x16) + 8 + (0x4) + (0x2) + (0x1)
= 128 + 64 + 8 = 200
1: 1
2: 10
3: 11
4: 100
5: 101
6: 110
7: 111
8: 1000
9: 1001
10: 1010
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What values can a bit take?
They are binary. They can be High (1) or low (0).Old joke: There are 10 types of people! Those that understand binary and those that do not.
What is 1 plus 1 in binary?
1 + 1 = 10 in binary numbers.
What is the binary code for 0?
Normally 1 - 1 = 0 the binary number for 1 is 1 the binary number for 2 is 10 the binary number for 3 is 11 3 - 2 = 1 The binary form of that equation is 11 - 10 = 1 The binary inverse operation would be 1 + 10 = 11 The rest is binary math 11 + 10 = 101 10 + 10 = 100 101 - 1 = 100 100 - 1 = 11 11 - 1 = 10 10 - 1 = 1 1 - 1 = 0 Therefore according to the pattern being displayed, the binary code for zero is 0.
What is the binary number 1111 in decimal?
The binary number 1111 is 15. The digits in a binary number are exponents of 2 rather than 10, so that for a four digit number in binary, the digit places represent 8, 4, 2, 1 instead of increasing values of 10. 1111 = 8+4+2+1 = 15
What is the decimal number 23 as a binary number?
The number 23 is 10111 in binary. The digits in a binary number are exponents of 2 rather than 10, so that for a five digit number in binary, the digit places represent 16, 8, 4, 2, 1 instead of increasing values of 10. 10111 = 16+0+4+2+1 = 23
What are the two possible values of a binary bit?
0 & 1
How many values are possible using a single binary digit?
Answer: 2The values are 0 or 1.
What is the binary number for 75?
The number 75 in binary is 1001011. The digits in a binary number are exponents of 2 rather than 10, so that for a seven digit number in binary, the digit places represent 64, 32, 16, 8, 4, 2, 1 instead of increasing values of 10. 1001011 = 64+0+0+8+0+2+1 = 75
What is the meaning of binary form?
Our system uses 10 numbers: 0123456789. Binary only uses 0 and 1. Our 1 is binary 1, but because there are no more numbers to use, our 2 is binary 10, our 3 is binary 11, our 4 is binary 100, and so on.
In the binary system what is 1 plus 1?
1 plus 1 = 2
How many unique values are possible using a single binary digit?
Answer: 2The values are 0 or 1.
6 How many values does a binary digit bit have?
It can have 0 to 1 It can have 0 to 1
