### A good answer might be:

Power of 2 | 3 | 2 | 1 | 0 | . | -2 | -3 | -4 | -5
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Decimal | 8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625
Include? |  | 1 | 0 | 0 | . | 0 | 1 |  |

`= 4.25`

# Fixed Point Notation

With paper-and-pencil arithmetic you can use as many digits or bits as are needed. But computers (usually) use a fixed number of bits for a particular data type. For example, MIPS integers are 32 bits. Can a fixed number of bits be used to express fractions?

Yes. Let us look briefly at an older method, not much used anymore. In the past, some electronic calculators and some computers used fixed point notation for expressing a fractional number. With fixed point notation, a number is expressed in a certain number of bits (say eight) and the binary point is assumed to be permanently fixed at a certain position.

For example, let us say that fixed point numbers uses eight bits and that the binary point is fixed between the middle two bits, like in the table. Now to interpret an eight-bit expression, just copy the bits to the table.

### QUESTION 7:

In this scheme, what does the bit pattern `01101001` represent in decimal?

Power of 2 | 3 | 2 | 1 | 0 | . | -2 | -3 | -4 | -5
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Decimal | 8 | 4 | 2 | 1 | . | 0.5 | 0.25 | 0.125 | 0.0625
Include? |  |  |  |  | . |  |  |  |

(Fill in the table.)