# Multi Precision

Each integer in the circuit has a certain bit-width, which is determined by the inputset. These bit-widths can be observed when graphs are printed:

However, it's not possible to add 3-bit and 4-bit numbers together because their encoding is different:

The result of such an addition is a 5-bit number, which also has a different encoding:

Because of these encoding differences, we perform a graph processing step called bit-width assignment, which takes the graph and updates the bit-widths to be compatible with FHE.

After this graph processing step, the graph would look like:

Most operations cannot change the encoding, which means that the input and output bit-widths need to be the same. However, there is an operation which can change the encoding: the table lookup operation.

Let's say you have this graph:

This is the graph for `(x**2) + y`

where `x`

is 2-bits and `y`

is 5-bits. If the table lookup operation wasn't able to change the encoding, we'd need to make everything 6-bits. However, since the encoding can be changed, the bit-widths can be assigned like so:

In this case, we kept `x`

as 2-bits, but set the table lookup result and `y`

to be 6-bits, so that the addition can be performed.

This style of bit-width assignment is called multi-precision, and it is enabled by default. To disable it and use a single precision across the circuit, you can use the `single_precision=True`

configuration option.

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