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Floating Point Binary
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This document contains notes on binary floating point numbers, including basic arithmetic, conversion to and from base-10, error calculations, signed floating point numbers, and more.
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Binary Arithmetic#computer-science #binary #bases #arithmetic
Addition
There are only five necessary operations in binary:
02 + 02 = 02
02 + 12 = 12
12 + 02 = 12
12 + 12 = 102
12 + 12 + 12 = 112
Carry Bits
In the last two cases above, the left-hand bit is a carry bit. There are
three options for dealing with these:
1. Carry it into the next calculation
2. Ignore it
3. Throw an exception
, Fixed Point Binary
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#computer-science #binary #bases #arithmetic
See also: Floating Point Binary
In denary, place values right of the decimal point have negative index
values . This is the same in binary
Index: 2 1 0 -1 -2 -3
3 4 1 . 1 0 2
This is base 10 ^^^
Index: 2 1 0 -1 -2 -3 -4 -5
0 1 0 . 1 0 1 1 0
Place 4 1 1/2 1/8 1/32
Value: 2 1/4 1/16
Result: = 2.6875 (base 10)
This representation works for both signed and unsigned integers.
An Issue
Some decimals, such as 0.1, cannot be represented exactly in binary.
0.12 ≡ 0.000110011001100110011. . .2
Fixed Point Representation
When encoding fractional numbers in binary, there are two main constraints:
1. There are a set number of bits available for encoding the data
2. There is no special character for where the binary point goes
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