A hexagram is a gram with six lines, either broken lines (0) or full lines(1).

The I Ching uses hexagrams for its main operations. There a 64 possible hexagrams.

Binary name:

000000 - 000001 - 000010 - 000011
000100 - 000101 - 000110 - 000111
001000 - 001001 - 001010 - 001011
001100 - 001101 - 001110 - 001111

010000 - 010001 - 010010 - 010011
010100 - 010101 - 010110 - 010111
011000 - 011001 - 011010 - 011011
011100 - 011101 - 011110 - 011111

100000 - 100001 - 100010 - 100011
100100 - 100101 - 100110 - 100111
101000 - 101001 - 101010 - 101011
101100 - 101101 - 101110 - 101111

110000 - 110001 - 110010 - 110011
110100 - 110101 - 110110 - 110111
111000 - 111001 - 111010 - 111011
111100 - 111101 - 111110 - 111111

Meanings:

You could assemble meanings with any of these templates (or come up with something new).

(monogram) of (pentagram)
(digram) of (quadgram)
(trigram) of (trigram)
(quadgram) of (digram)
(pentragram) of (monogram)

Mapping examples:

(the common translation of the I Ching hexagram names)

field - returning - leading - nearing
humbling - brightness hiding - ascending - prevading
providing for - shake - taking apart - converting the maiden
small exceding - abounding - persevering - great invigorating

grouping - sprouting - gorge - articulating
limping - already fording - welling - attending
clustering - following - confining - open
conjoining - skinning - great exceeding - parting

stripping - swallowing - enveloping - diminishing
bound - adorning - corrupting - great accumulating
prospering - gnawing bite - not yet fording - polarising
sojourning - radiance - holding - great possessing

viewing - augmenting - dispersing - centre confirming
infiltrating - dwelling people - ground - small accumulating
obstruction - without embroiling - arguing - treading
retiring - concording people - coupling - force

In the I Ching, a hexagram is composed of two trigrams: the lower trigram emphasizes the inner aspect, and the upper trigram emphasizes the outer aspect.