# Binary Calculator

Not only in mathematics but also in digital electronics, one comes across the binary number which is said to be a number expressed either in binary numeral system or the base 2 numeral system as it turns out to be a representation of 0s as well as 1s.

## How to use a binary calculator?

Using a binary calculator is easy when it comes to any one of the following that are – addition / subtraction / multiplication / division. And if you wish to take up any one of the following things then the following steps will guide you to success. In the 1st field, you would be required to enter the binary number that too without any spaces or commas or fractions. This will be followed by the selection of the operator & again enter the binary number before clicking on calculate to get the result.

## Decimal to Binary Calculator

 Decimal value: Binary value:

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## How to convert binary value to a decimal value?

When it comes to conversion of the binary value to a decimal value, it does not take a lot of effort to get the results, one will have to firstly enter the binary value which is to be converted & then click on the tab that reads calculate.

### Binary to decimal example (formula)

 128 64 32 16 8 4 2 1 1 0 0 1 1 1 0 1

In the above formula we can see that the numbers such as 1, 2, 4, 8, 16, 32, 64 and 128 [all are powers of 2] have been placed in the reverse numerical order while the binary values have been given below. Thus, if you have to convert binary value to a decimal value, you would be required to take a certain value from the 1st row (at a point where there is number 1 below & after this you would have to add the values.

$$E.g. \quad 128+16+8+4+1=157$$

For 16 bit value, decimal values like the following can be put in to use [which are again powers of 2] for conversion.

$$E.g. \quad 1,\quad 2,\quad 4,\quad 8,\quad 16,\quad 32,\quad 64,\quad 128,\quad 256,\quad 512,\quad 1024,\quad 2048,\quad 4096,\quad 8192,\quad 16384,\quad 32768.$$

As binary is base 2, the above equation can be written in the following format –

$$1\times 2^7+0 \times 2^6+0 \times 2^5+1 \times 2^4+1 \times 2^3+1\times 2^2+0 \times 2^1+1\times 2^0=157$$

## Steps to convert the decimal value to a binary value

Finally when it comes to the conversion of a decimal value to a binary value, similar steps as seen above are to be followed. Hence, the user should 1st enter the decimal value & then click on the tab which says calculate. This way they will be in a position to get the result.

When you are using this binary calculator, you will have to remember the fact that the values entered are correct & in the proper format in order to avoid errors. To understand the decimal to binary formula, the equation given below will be helpful.

$$E.g. \quad \frac{157}{2}=\quad 78 \quad with \quad a \quad remainder \quad of \quad 1$$

$$\frac{78}{2}=\quad 39 \quad with \quad a \quad remainder \quad of \quad 0$$

$$\frac{39}{2}=\quad 19 \quad with \quad a \quad remainder \quad of \quad 1$$

$$\frac{19}{2}=\quad 9 \quad with \quad a \quad remainder \quad of \quad 1$$

$$\frac{9}{2}=\quad 4 \quad with \quad a \quad remainder \quad of \quad 1$$

$$\frac{4}{2}=\quad 2 \quad with \quad a \quad remainder \quad of \quad 0$$

$$\frac{2}{2}=\quad 1 \quad with \quad a \quad remainder \quad of \quad 0$$

$$\frac{1}{2}=\quad 0 \quad with \quad a \quad remainder \quad of \quad 1$$

Hence, if you wish to convert then the last remainder that is 1 is to be written first followed by the others. And if at all you will have to check whether the answer is right or not then the binary to decimal formula is useful.

### Binary arithmetic – Addition

$$E.g. \quad 0+0\rightarrow0$$

$$0+1\rightarrow1$$

$$1+0\rightarrow1$$

$$1+1\rightarrow0 , \quad carry \quad 1 \quad (since \quad 1+1=\quad 2 \quad =0+\quad (1 \times 2^{1}))$$

$$E.g. \quad 1 \quad 1 \quad 1 \quad 1 \quad 1 \quad (carried \quad digits)$$

$$0\quad 1\quad 1\quad 0 \quad 1\quad$$

$$+\quad 1\quad 0 \quad 1\quad 1 \quad 1\quad$$

————————-

$$=\quad 1\quad 0\quad 0\quad 1 \quad 0\quad 0= \quad 36$$

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### Addition table (formula)

 0 1 10 11 100 0 0 1 10 11 100 1 1 10 11 100 101 10 10 11 100 101 110 11 11 100 101 110 111 100 100 101 110 111 1000

### Binary arithmetic – subtraction

$$E.g.\quad 0 – 0 \rightarrow 0$$

$$0 – 1 \rightarrow\quad 1,\quad borrow \quad 1$$

$$1 – 0 \rightarrow\quad 1$$

$$1 – 1 \rightarrow\quad 0$$

$$* \quad \quad \quad *\quad *\quad * \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad (starred columns are borrowed from)$$

$$1 \quad1\quad 0 \quad1 \quad1 \quad1 \quad0$$

–  $$1 \quad 0 \quad 1 \quad 1 \quad 1$$

———————–

$$=\quad 1\quad 0 \quad 1 \quad 0\quad 1\quad 1\quad 1$$

———————–

$$1\quad 0\quad 1\quad 1\quad 1\quad 1\quad 1$$

$$- \quad 1 \quad 0 \quad 1\quad 0\quad 1\quad 1$$

——————-

$$= \quad0 \quad1 \quad1 \quad0 \quad1\quad 0 \quad0$$

——————-

### Multiplication, binary arithmetic

$$1 \quad 0 \quad 1 \quad 1 \quad \quad (A)$$

$$\times \quad 1\quad 0\quad 1\quad 0 \quad \quad (B)$$

———————–

$$0\quad 0 \quad0 \quad0 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \leftarrow Corresponds \quad to\quad rightmost\quad ‘0’\quad in\quad B$$

$$1\quad 0 \quad1 \quad1 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \leftarrow Corresponds \quad to\quad next\quad ‘1’\quad in\quad B$$

$$+0\quad 0\quad 0 \quad 0$$

$$+1\quad 0\quad 1 \quad 1$$

——————

$$= 1\quad 1\quad 0 \quad1 \quad1 \quad1 \quad0$$

——————

### Multiplication table

 0 1 0 0 0 1 0 1

### Division, binary arithmetic

$$eq$$