Editing Balanced ternary (section)

=== Conversion from unbalanced ternary ===
Unbalanced ternary can be converted to balanced ternary notation in two ways: 
*Add 1 trit-by-trit from the first non-zero trit with carry, and then subtract 1 trit-by-trit from the same trit without borrow. For example,
*: 021<sub>3</sub> + 11<sub>3</sub> = 102<sub>3</sub>, 102<sub>3</sub> − 11<sub>3</sub> = 1T1<sub>bal3</sub> = 7<sub>dec</sub>.
*If a 2 is present in ternary, turn it into 1T. For example,
*: 0212<sub>3</sub> = 0010<sub>bal3</sub> + 1T00<sub>bal3</sub> + 001T<sub>bal3</sub> = 10TT<sub>bal3</sub> = 23<sub>dec</sub>

{| class="wikitable floatright" style=" text-align: center"
|-
! Balanced || Logic   || Unsigned
|-
| 1        || True    || 2
|-
| 0        || Unknown || 1
|-
| T        || False   || 0
|}
If the three values of [[Three-valued logic#Kleene logic|ternary logic]] are ''false'', ''unknown'' and ''true'', and these are mapped to balanced ternary as T, 0 and 1 and to conventional unsigned ternary values as 0, 1 and 2, then balanced ternary can be viewed as a biased number system analogous to the [[offset binary]] system.
If the ternary number has ''n'' trits, then the bias ''b'' is
:<math>b=\left\lfloor \frac{3^n}{2} \right\rfloor</math>
which is represented as all ones in either conventional or biased form.<ref>Douglas W. Jones, [http://www.cs.uiowa.edu/~jones/ternary/numbers.shtml Ternary Number Systems], October 15, 2013.</ref>

As a result, if these two representations are used for balanced and unsigned ternary numbers, an unsigned ''n''-trit positive ternary value can be converted to balanced form by adding the bias ''b'' and a positive balanced number can be converted to unsigned form by subtracting the bias ''b''.  Furthermore, if ''x'' and ''y'' are balanced numbers, their balanced sum is {{nowrap|''x'' + ''y'' − ''b''}} when computed using conventional unsigned ternary arithmetic. Similarly, if ''x'' and ''y'' are conventional unsigned ternary numbers, their sum is {{nowrap|''x'' + ''y'' + ''b''}} when computed using balanced ternary arithmetic.