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Binary (BIN)
The binary number system consists of two symbols: 0 and 1 which represent
the order and size (amount). After a digit reaches 1, an increment is reset to 0
and the next digit (to the left) is incremented. The two digits 0 and 1 are called
bits.
Binary Decimal
0 0
1 1
10 2
11 3
100 4
101 5
110 6
111 7
1000 8
…
…
The following example explains how to convert a binary number into a decimal
number.
"10011101"
The diagram below shows the binary number with the powers of two.
1
7
2
7
128
0
6
2
6
64
0
5
2
5
32
1
4
2
4
16
1
3
2
3
8
1
2
2
2
4
0
1
2
1
2
1
0
2
0
1
Bit number
Binary
Base number raised
to the power of digit
("Binary")
= Bit weights
The binary number is broken as follows.
= 1 × 128
+ 0 × 64 + 0 × 32 + 1 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1
= 128 + 16 + 8 + 4 + 1
= 157
The binary number can be calculated by adding each weight of bits whose
codes are 1.