## 1.6 Converting Binary Numbers into Decimal

1.6 Converting Binary Numbers into Decimal

To convert a binary number into decimal, write the number as the sum of the powers of 2.

### Example 1.1

Convert binary number 10112 into decimal.

### Solution 1.1

Write the number as the sum of the powers of 2:

10112 = 1 ? 23 + 0 ? 22 + 1 ? 21 + 1 ? 20

= 8 + 0 + 2 = 1

= 11

or, 10112 = 1110

### Example 1.2

Convert binary number 110011102 into decimal.

### Solution 1.2

Write the number as the sum of the powers of 2:

110011102 = 1 ? 27 + 1 ? 26 + 0 ? 25 + 0 ? 2+ 1 ? 23 + 1 ? 22 + 1 ? 21 + 0 ? 20

= 128 + 64 + 0 + 0 + 8 + 4 + 2 + 0

= 206

or, 110011102 = 20610

Table 1.1 shows the decimal equivalent of numbers from 0 to 31.

Table 1.1: Decimal equivalent of binary numbers

Binary Decimal Binary Decimal
00000000 0 00010000 16
00000001 1 00010001 17
00000010 2 00010010 18
00000011 3 00010011 19
00000100 4 00010100 20
00000101 5 00010101 21
00000110 6 00010110 22
00000111 7 00010111 23
00001000 8 00011000 24
00001001 9 00011001 25
00001010 10 00011010 26
00001011 11 00011011 27
00001100 12 00011100 28
00001101 13 00011101 29
00001110 14 00011110 30
00001111 15 00011111 31

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