What Is The Binary Equivalent Of The Decimal Number 232?

What Is The Binary Equivalent Of The Decimal Number 232?

11101000 is the binary equivalent of the decimal number 232. Now, let us discuss how the binary equivalent of the decimal number 232 is found. For suppose if any decimal number is given that to convert into binary, where 232 is the decimal number that we have taken, now we have to find the binary equivalent of the number.

When we are going to convert decimal to any other form, we need to perform the division with the respective number that is taken. The conversion of decimal to decimal is nothing but the power of 2 from the left to right. We can perform this conversion in two methods. The first is the subtraction method and division method. Firstly, let us discuss the subtraction method.

128 64 32 16 8 4 2 1

The above is the sequence of power of 2. Here we do not need to go further to power 2 because the decimal 232 can be found with the above sequence. Now, we are going to add the values that give the sum value equal to the decimal number.

First, fill the number with 1 which has the lowest value after the decimal number 232 in the sequence. Then we get as

128 64 32 16 8 4 2 1

1

Here, after we fill the 128 with 1, the remaining sum which we need to find is 232-128 = 104. And the next lowest number after 104 is 64.

128 64 32 16 8 4 2 1

1         1

After we add 128+ 64 = 192, still we need to add 40 to reach the binary number of 232. So we need to find the next lowest number than 40, that is 32. when we add 32 we get 128+64+32=224

128 64 32 16 8 4 2 1

1       1       1

By subtracting the method, 232-224=8, we know that we need to add 8 more to reach the binary equivalent of the decimal number 232.

128 64 32 16 8 4 2 1

1         1

Now, we got to reach the binary number of 232. Here we have to give the remaining values as 0 which we have not included in the sequence.

128 64 32 16 8 4 2 1

1      1      1     0   1  0  0   0

Hence, the above sequence is the binary equivalent of the decimal number 232.

Now, let us find binary equivalent using the division method. In the division method, we have to divide the number by 2, we get

232 divided by 2 = 232/2 , remainder = 0 and quotient = 116

now, again divide the quotient with 2 116/2, remainder = 0, and quotient=58.

similarly, 58/2, remainder = 0 and quotient = 29

29/2, remainder = 0 and quotient = 14

14/2, remainder = 0 and quotient = 7

7/2, remainder = 1 and quotient = 3

3/2, remainder = 1 and quotient = 1

1/2, remainder = 1 and quotient = 1

Here when take all the remainders from bottom to top, we get the binary equivalent of the decimal number. Then, 1 1 1 0 1 0 0 0.