Amit Singh Tomar - 1 year ago 144

C Question

While reading a tutorial I came across how to represent Float number in memory. The tutorial had an example with a floating point number.

`float a=5.2 with below Diagram`

Can anyone please tell how this 5.2 is converted in to binary and how it is represented in memory in above the above diagram?

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Answer Source

As was said, 5.2 is represented as a sign bit, an exponent and a mantissa. How do you encode 5.2?

5 is easy:

```
101.
```

The rest, 0.2 is 1/5, so divide `0.FFFFFFF...`

(hex) by 5 (or `1.00000...`

(hex)) and you get `0.3333333...`

(hex).

That should give you

```
0.0011001100110011001100110011...
```

Add 5, and you get

```
101.00110011001100110011... exp 0 (5.2 * 2^0)
```

Now shift it (normalize it) and adjust the exponent accordingly

```
1.010011001100110011001100110011... exp +2 (1.3 * 2^2)
```

Now you only have to add the bias of 127 (i.e. `129 = 0b10000001`

) to the exponent and store it:

```
0 10000001 1010 0110 0110 0110 0110 0110
```

Forget the top 1 of the mantissa (which is always supposed to be 1, except for some special values, so it is not stored), and you get:

```
01000000 10100110 01100110 01100110
```

Now you only have to decide little or big endian.

This is not exactly how it works, but that is more or less what happens when a number like 5.2 is converted to binary.

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