SECTION I-3: Converting from Binary to Decimal

To convert from Binary to Decimal, it is important to understand the concept of weight associated with each digit position. Recall the weight of numbers in the Base 10 system. Each digit position of a number in Base 2 has a weight associated with it.

74068310
3X100 = 3
8X101 = 80
6X102 = 600
0X103 = 0000
4X104 = 40000
7X105 = 700000
TOTAL 740683
1101012 Decimal Binary
1X20 = 1X1 = 1 1
0X21 = 0X2 = 0 00
1X22 = 1X4 = 4 100
0X23 = 0X8 = 0 0000
1X24 = 1X16 = 16 10000
1X25 = 1X32 = 32 110101
TOTAL 53 110101
Convert 110012
Weight   16     8     4     2     1  
Digits 1 1 0 0 1
Total 16+ 8+ 0+ 0+ 1
= 2510

Knowing the weight associated with each binary bit position allows one to convert a decimal number to binary directly instead of going through the process of repeated division. This is demonstrated below.

Convert 3910 to Binary
Weight 32 16 8 4 2 1
Digits 1 0 0 1 1 1
Total 32+ 0+ 0+ 1+ 1+ 1
= 3910 Therefore, 3910 = 1001112

 

 

 

 

 

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