can u please show me how to write an algorithm with a flow chart that converts a positive decimal number to an unsigned binary number.

Question

i want the flow chart not the code

Answer 1

First we need to build the table that contains the powers of 2.

So how many binary bits does the number require? Let's say we are converting 32 bit whole

number and 32 bit decimal number.

So we need 32 bit array of bits for the whole number and 32 bit array of the decimal number.

2^32 = 4294967296 = bits[32]

2^31 = 2147483648 = bits[31]

2^30 = 1073741824= bits[30]

2^29 = 536870912=bits[29]

2^28 = 268435456 - bits[28]

....

2^15 = 32768 = bits[15]

....

2^8 = 256 = bits[8]

2^7 = 128 = bits[7]

2^6 = 64 = bits[6]

2^5 = 32 = bits[5]

2^4 = 16 = bits[4]

2^3 = 8 = bits[3]

2^2 = 4 = bits[2]

2^1 = 2 = bits[1]

2^0 = 1 = bits[0]

Then you do the same for the decimal number

2^0 = 1 = bits[0]

2^(-1) = 0.5 = bits[1] <--- 1/2

2^(-2) = 0.25 = bits[2] <--- 1/4

2^(-3) = 0.125 = bits[3] <--- 1/8

2^(-4) = 0.0625 = bits[4] <---- 1//16

etc

Next you separate the whole number from the decimal part.

Assign the whole number to variable X and decimal to variable Y

for each bit in the whole number, i=32 to 1

if X > bits(i) then

sets that bit to 1

subtracts X = X - bit(i)

else

sets that bit to zer0

end if

end for loop

So basically, if the remainder that's left is greater than the bit value, you set the bit to 1;

otherwise, you set it to zer0

for each bit in the decimal number, i=1 to 32

if Y > bits(i) then

sets that bit to 1

subtracts X = X - bit(i)

else

sets that bit to zer0

end if

end for loop

======================

Here is an example:

123.789

the highest power of 2 is 128 = 2^7. each bit before that shall be zero

So starting with bit 7, which will be zero.

bit # value bit set X - bit value

7 128 0 123

6 64 1 59

5 32 1 27

4 16 1 11

3 8 1 3

2 4 0 3

1 2 1 1

0 1 1 0

So the decimal portion is 01111011

the decimal is Y=0.789

bit # value bit set Y - bit value

1 0.5 1 0.289

2 0.25 1 0.039

3 0.125 0 0.039

4 0.0625 0 0.039

5 0.03125 1 0.00775

6 0.015625 0 0.00775

7 0.0078125 0 0.00775

8 0.00390625 1 0.0384375

9 0.00390625 0 0.0384375

10 0.001953125 1 0.036484375

etc

https://www.geeksforgeeks.org/convert-decimal-fraction-binary-number/