# Fixed Point Numbers

## The Binary Point

Fixed Point numbers are a straightforward and simple approach to express Fractional numbers, utilizing a Fixed Number of bits.

The expression "Fixed Point" alludes to the position of the Binary Point. The Binary Point is similar to the Decimal Point of a base-ten number, however since this is Binary as opposed to Decimal, an alternate term is utilized. In Binary, bits can be either 0 or 1 and there is no different image to assign where the Binary Point lies. Be that as it may, we envision, or accept, that the Binary Point lives at a Fixed area between assigned bits in the number.

For example, in a 32-bit number, we can expect that the Binary Point exists specifically between bits 15 (15 in light of the fact that the primary piece is numbered 0, not 1) and 16, giving 16 bits for the Whole number part and 16 bits for the Fractional part. Note that the most significant bit in the whole number field is generally designated as the sign bit leaving 15 bits for the whole number's magnitude.

## Place Value Method

Not all numbers can be represented exactly by a fixed-point number, and so the closest approximation is used.

In the above example the number stored would be : 32 + 8 + 2 + 1 + 0.25 + 0.03125 + 0.0078125 + 0.00390625 = 43.2869375

## Repeated Multiplication

You can convert any decimal fraction to a binary fraction. Multiply the fractional part of the number by 2. Take the integer part of the result (1 or 0) as the first bit. Repeat this process with the result until you run out of patience. For example, to convert 0.3568 into fixed point binary with 8 bits to the right of the binary point,

0.3568 is .01011011

# Revision

1. What is the correct binary for the number 15.375?

 1111.0110 → 1111 = 15 0110 = 0.25 0110 = 0.0625 0.25 + 0.0625 = 0.3125 1101.1010 → 1101 = 13 1010 = 0.5 1010 = 0.125 0.5 + 0.125 = 0.625 1001.1001 → 1001 = 9 1001 = 0.5 1001 = 0.0625 0.25 + 0.0625 = 0.5625 0111.1011 → 0111 = 7 1011 = 0.5 1011 = 0.125 1011 = 0.0625 0.5 + 0.125 + 0.0625 = 0.6875

2. What is the correct binary for the number 13.1875?

 1111.0101 → 1111 = 15 .0101 = 0.3125 1011.1111 → 1011 = 11 .1111 = 0.9375 1010.0111 → 1010 = 10 .0111 = 0.4375 1101.0011 → 1101 = 13 .0011 = 0.1875

3. Convert 7.78125 into binary.

 111.01100 → 111 = 7 .01100 = 0.375 111.11001 → 111 = 7 .11001 = 0.78125 100.01001 → 100 = 4 .01001 = 0.28125 101.01101 → 101 = 5 .01101 = 0.40625

4. convert 1111.1010 into denary

 15.625 → 15 = 1111 .625 = 1010 11.375 → 11 = 1011 .375 = 0110 13.725 → 13 = 1101 .725 = 1011 10.855 → 10 = 1010 .855 = 1101

5. What is the correct binary for the number 10.5

 110 101.11 1010.1 1110.1

6. What is 0101.0101 in denary ?

 5.3125 12.9678 7.8665 3.3455 → Denary is the standard number system

7. Is 0011.1000, 3.5 in Denary ?

 Yes No

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