# Convert from decimal to binary

### Decimal Repeated division by 2

| 2 | 43 | | | 2 | 21 rem 1 | <- LSB | | 2 | 10 rem 1 | | | 2 | 5 rem 0 | | | 2 | 2 rem 1 | | | 2 | 1 rem 0 | | | 0 | rem 1 | <- MSB |

2nd column forms 101011.

### Fraction - repeated multiplication by 2

Carried digits produce answer: *1*.000 (1 is the carried digit here)

| 0.3125 * 2 = 0.625 | 0 | | 0.625 * 2 = 1.25 | 1 | | 0.25 * 2 = 0.50 | 0 | | 0.5 * 2 = 1.00 | 1 |

( 0.3125 ) 10 = (.0101) 2

### Sum of weights

Determine set of binary weights whose sum == decimal number 9 = 8 + 1 = 1001 18 = 16 + 2 = 10010 58 = 32 + 16 + 8 + 2 = 111010