Linary Timepiece uses Linary Numeral System, base four positional system for expressing numbers using the following symbols called Linits:
Linit 

Value 
0 
1 
2 
3 
Any number can be expressed in Linary system by expressing it in the form:
l_{n}4^{n} + l_{n – 1}4^{n  1} + l_{n – 2}4^{n  2} + ... + l_{0}4^{0}
where enumerated linits l_{n}l_{n  1}l_{n  2 }... l_{0} are in descending order and have values between 0 and 3 expressed using symbols defined in the above table.
Linary numeral system can be easly encoded (or decoded) by grouping a number expressed in binary digits by two and drawing a line between the two binary digits in a group in such a way that if a binary number has a vluae of 0 the end of a line (linit) representing this binary digit is in a lower position, if a binary number has a vlaue of one, the end of the line (linit) representing this digit is in a higher position. Each linit in the linary system represents a group of two binary digits and the position of each end of the linit represents the value of each binary digit within the group.
Linary numeral system and its relationship to binary system:
Linit 

binary value 
2^{n} 2^{n1} 
2^{5} 2^{4} 
2^{3} 2^{2} 
2^{1} 2^{0} 
Because a group of two binary numbers can have four values (00,01,10,11)
a linit representing the two binary digits can have the following four shapes:,,,, as defined in the first table.
Example:
In the above example:
Seconds, represented by  =  11 00 11 (binary) = 1*2^{5}+1*2^{4}+0*2^{3}+0*2^{2}+1*2^{1}+1*2^{0} = 32+16+0+0+2+1 = 51 seconds or in base 4 notation: 3*4^{2}+0*4^{1}+3*4^{0}= 48 + 0 + 3 = 51  
Hours, represented by  =  01 00 (binary) = 0*2^{3}+1*2^{2}+0*2^{1}+0*2^{0} = 0 + 4 + 0 + 0 = 4 O'Clock or in base 4 notation: 1*4^{1}+0*4^{0} = 4 + 0 = 4  
Minutes, represented by  =  10 10 10 (binary) = 1*2^{5}+0*2^{4}+1*2^{3}+0*2^{2}+1*2^{1}+0*2^{0} = 32+0+8+0+2+0 = 42 minutes or in base 4 notation: 2*4^{2}+2*4^{1}+2*4^{0} = 32+8+2 = 42  
Day of a month, represented by  =  00 11 00 (binary) = 0*2^{5}+0*2^{4}+1*2^{3}+1*2^{2}+0*2^{1}+0*2^{0} = 0+0+8+4+0+0 = 12^{th} day or in base 4 notation: 0*4^{2}+3*4^{1}+0*4^{0}= 0 + 12 + 0 = 12 
To see a live example click here
Android wearable linary watch: Google Play
Linary Numeral System is a patent pending application
First 25 values expressed in linary notiation:
Decimal 
Linary 
Binary 
0 
000000 

1 
000001 

2 
000010 

3 
000011 

4 
000100 

5 
000101 

6 
000110 

7 
000111 

8 
001000 

9 
001001 

10 
001010 

11 
001011 

12 
001100 

13 
001101 

14 
001110 

15 
001111 

16 
010000 

17 
010001 

18 
010010 

19 
010011 

20 
010100 

21 
010101 

22 
010110 

23 
010111 

24 
011000 

25 
011001 