Question

Convert decimal number 45.5 to binary using sum of weights method

Answer 1

To convert given decimal number to binary split it into two parts

one before decimal:

By dividing the number by two in integer form and put remainder aside

2 ) 45 (1
****44
_______
2 ) 22 (0
****22
______
2 )11(1
***10
_______
2 ) 5(1
****4
_______
2)2(0
***2
______
***1

So, 45 is written into binary as 101101

Now conversion of 0.5:
0.5×2 = 1.0
0.0×2= 0.0

So it is .10

Now the complete number is

45.5 decimal = 101101.1 in binary

Verification:

$1 \: \: 0 \: \: 1 \: \: 1 \: \: 0 \: \: 1 \: \: .1 \\ \\ {2}^{5} \times 1 + \: \: {2}^{3} \times 1 + \: \: {2}^{2} \times 1 + \: \: {2}^{0} + \: . 1 \times {2}^{ - 1} \\ \\ 32 + 8 + 4 + 1 + .5 \\ \\ 45.5$