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Binary (base 2) to Senary (base 6)

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In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit.

conversion table

binary (base 2)senary (base 6)binary (base 2)senary (base 6)
1= 11011= 15
10= 21100= 20
11= 31101= 21
100= 41110= 22
101= 51111= 23
110= 1010000= 24
111= 1110001= 25
1000= 1210010= 30
1001= 1310011= 31
1010= 1410100= 32

The senary numeral system (also known as base-6 or heximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though being the product of the only two consecutive numbers that are both prime (2 and 3) it has a high degree of mathematical properties for its size. As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6.

conversion table

senary (base 6)binary (base 2)senary (base 6)binary (base 2)
1≈ 115≈ 1011
2≈ 1020≈ 1100
3≈ 1121≈ 1101
4≈ 10022≈ 1110
5≈ 10123≈ 1111
10≈ 11024≈ 10000
11≈ 11125≈ 10001
12≈ 100030≈ 10010
13≈ 100131≈ 10011
14≈ 101032≈ 10100