3. Decimal to binary conversion:
Method of division by two
Decimal to binary conversion is based on the fact that a decimal number can be
represented as
d=an2^n+a(n-1)2^(n-1)+a(n-2)2^(n-2).........a(1)2^(1)+a(0)2^(0)
Eg 9=1*2^3 + 0*2^2 + 0*2^1 + 1*2^0
If we divide it by two we get the quotient as
q=d/2=a(n)2^(n-1)+a(n-1)2^(n-2)+a(n-2)2^(n-3).........+a(1)
and remainder r =a0(a0 is the least significant digit of the binary number.)
We again divide the quotient by two the
q/2=d/4=a(n)2^(n-2)+a(n-1)2^(n-3)+a(n-2)2^(n-4).........+a(2)
and the remainder =a1

4. Method of division by 2 continued
We continue this process until the quotient becomes zero.
Eg 19=d= 1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0
q=d/2= 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0
r1=1
q/2=d/2*2=1*2^2 + 0*2^1 + 0*2^0
r2=1
q/2*2=d/2*2*2= 1*2^1 + 0*2^0
r3=0
q/2*2*2=d/2*2*2*2=1*2^0
r4=0
q/2*2*2*2=d/2*2*2*2*2=0
r5=1
Thus the binary equivalent of 19 is 10011.

5. Division by 2 algorithm
var
D:integer {D is the decimal integer that is to be converted to binary};
B:bitstring{B stores the binary equivalent of D};
Q,R:integer{intermediate variables used in conversion};
input D;
b:null;
if(D=0) then begin B:=0 goto 10 end;
while (D!=0)do
begin
Q:=D div 2 {D div 2 gives the quotient of D/2}
R:=D mod 2;
B=concatenate to left (R,B);
D:=Q
end;
10:Output B;
end{of algorithm}

6. Converting decimal fraction to binary
To convert a decimal fraction to binary we use repeated division on the
integral part and repeated multiplication on the decimal part. Suppose we
want to convert (11.625)10 binary . We find the binary equivalent of 11 by
repeated division and binary equivalent of 625 by repeated multiplication.
The process of repeated multiplication is explained below.
Step 1. Multiply the decimal part by 2. The whole number part of the result
becomes the first number to right of the decimal point .
.625*2=1.25
so the first number to the right is 1
step 2 . We take the decimal part of the result and again multiply it by two .
.25*2=.050
So the second number to the right is 0.

7. Converting decimal fraction to binary continued
step 3. We take the decimal part of the result and again multiply it by 2
.50*2= 1.00
So the third number to the right of the decimal point is 1.
Step.4 There is no need for step 4 as the fractional part has become
zero.
So our answer becomes 1011.101

8. Converting decimal fraction to binary :Algorithm
var
D:real {D is the decimal fraction to be converted to binary};
B:Bitstring {Binary equivalent of D};
P:real {P is a intermediate variable used during conversion};
INTP:Bit{integer part of 9 which can either be 0 or 1};
begin {of algorithm}
input D;
B:=0 .null {null is a null string};
if(D=0) then begin B:=0; goto 10 end;
while(D!=0) and length (B)<=9 do
{length (B) returns the length of B and we have limited it to 9}
begin
P:=D*2;
INTP:=Trunc(P){Trunc P returns the integer part of P};