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 | |||||||||||