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[SOLVED] question of decimal to binary

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moonnightingale

moonnightingale

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the book says

(1.75) to the base 10 = (0001.1100) to the base 2

kindly explain this to me
 

To the left of the decimal point the binary values are 1 2 4 8 etc. To the right they are 0.5 0.25 0.125 etc. so the 0.75 is 0.5 + 0.25 so 0.11 in binary.

Keith
 

1.75
first the decimal part take it a lone
1 converted to binary is 0001

then we have fraction .75
.75 * 2 (binary system) = 1.5 (larger than 1 so) 1 and still have fraction of 1.5 -1 =.5
.5 * 2 = 1 equal one =1 fraction remainder is zero so
0001.110000
and to make the reverse
simply
00001
0*2^4+0*2^3+0*2^2+0*2^1+0*2^0 =1 decimal

.1100
1*2^(-1)+1*(2-2)+0*2^-3+000
=.75 decimal

for examples you can check digital design for mores mano first chapter
 
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