números fraccionaris binaris

(0.01)_{b} = (01/100)_{b} = (1/4)
(0.10)_{b} = (10/100)_{b} = (2/4) = (1/2)
(0.11)_{b} = (11/100)_{b} = (3/4)


(0.001)_{b} = (001/1000)_{b} = (1/8)
(0.010)_{b} = (010/1000)_{b} = (2/8) = (1/4)
(0.011)_{b} = (011/1000)_{b} = (3/8)
(0.100)_{b} = (100/1000)_{b} = (4/8) = (1/2)
(0.101)_{b} = (101/1000)_{b} = (5/8)
(0.110)_{b} = (011/1000)_{b} = (6/8) = (3/4)
(0.111)_{b} = (111/1000)_{b} = (7/8)


(100)_{b}·x+(-1)·x=(11)_{b}·x
(0.01...)_{b} = (1/3)
(0.10...)_{b} = (2/3)
(0.11...)_{b} = (3/3)


(1000)_{b}·x+(-1)·x=(111)_{b}·x
(0.001...)_{b} = (1/7)
(0.010...)_{b} = (2/7)
(0.011...)_{b} = (3/7)
(0.100...)_{b} = (4/7)
(0.101...)_{b} = (5/7)
(0.110...)_{b} = (6/7)
(0.111...)_{b} = (7/7)


(0.0011...)_{b} = (3/15) = (1/5)
(0.0110...)_{b} = (6/15) = (2/5)
(0.1001...)_{b} = (9/15) = (3/5)
(0.1100...)_{b} = (12/15) = (4/5)
(0.1111...)_{b} = (15/15) = (5/5)


(0.000111...)_{b} = (7/63) = (1/9)
(0.001110...)_{b} = (14/63) = (2/9)
(0.010101...)_{b} = (21/63) = (3/9) = (1/3)
(0.011100...)_{b} = (28/63) = (4/9)
(0.100011...)_{b} = (35/63) = (5/9)
(0.101010...)_{b} = (42/63) = (6/9) = (2/3)
(0.110001...)_{b} = (49/63) = (7/9)
(0.111000...)_{b} = (56/63) = (8/9)
(0.111111...)_{b} = (63/63) = (9/9)


(0.1)_{b}·(0.0011...)_{b} = (1/10)
(0.1)_{b}·(0.0110...)_{b} = (2/10)
(0.1)_{b}·(0.1001...)_{b} = (3/10)
(0.1)_{b}·(0.1100...)_{b} = (4/10)
(0.1)_{b}·(0.1111...)_{b} = (5/10) = (1/2)
(0.1)_{b}·(1.0011...)_{b} = (6/10)
(0.1)_{b}·(1.0110...)_{b} = (7/10)
(0.1)_{b}·(1.1001...)_{b} = (8/10)
(0.1)_{b}·(1.1100...)_{b} = (9/10)
(0.1)_{b}·(1.1111...)_{b} = (10/10)


(1/10)+1 = (0.1)_{b}·(10.0011...)_{b}
(1/10)+2 = (0.1)_{b}·(100.0011...)_{b}
(1/10)+3 = (0.1)_{b}·(110.0011...)_{b}
(1/10)+4 = (0.1)_{b}·(1000.0011...)_{b}


1+(-1)·(1/10) = (0.1)_{b}·(01.1100...)_{b}
2+(-1)·(1/10) = (0.1)_{b}·(011.1100...)_{b}
3+(-1)·(1/10) = (0.1)_{b}·(101.1100...)_{b}
4+(-1)·(1/10) = (0.1)_{b}·(0111.1100...)_{b}


(0.1)_{b}·(0.01...)_{b} = (1/6)
(0.1)_{b}·(0.10...)_{b} = (2/6) = (1/3)
(0.1)_{b}·(0.11...)_{b} = (3/6) = (1/2)
(0.1)_{b}·(1.01...)_{b} = (4/6) = (2/3)
(0.1)_{b}·(1.10...)_{b} = (5/6)
(0.1)_{b}·(1.11...)_{b} = (6/6)


(0.0001011101...)_{b} = (93/1023) = (1/11)