3 10 x 10 x 10 = 1000 = 10 3 2.32 x 10 = 2.32 x 1000 = 2320 1 light year = 12 9.454 x 10 km ~ 1 light year 9454000000000 km = 1 light year 100 light years = 945400000000000 km x 100 1 LY = 9454000000000 KM 100 LY = 945400000000000 KM 14 9.454 x 10 km ~ 100 light year Computers work with base 2 (binary) -------------------------- Binary Decimal ----------- ------- 1 1 10 2 100 4 1000 8 10000 16 100000 32 1000000 64 10000000 128 100000000 256 1000000000 512 10000000000 1024 0 1 x 2 = 1 x 1 = 1 1 1 x 2 = 1 x 2 = 2 2 1 x 2 = 1 x 4 = 4 3 1 x 2 = 1 x 8 = 8 4 1 x 2 = 1 x 16 = 16 -------------------------------------- 0 1.0 x 2 = 1 x 1 = 1 1 1.0 x 2 = 1 x 2 = 2 2 1.0 x 2 = 1 x 4 = 4 3 1.0 x 2 = 1 x 8 = 8 4 1.0 x 2 = 1 x 16 = 16 .... looks like scientific notation -------------------- Binary Decimal ------ ------- 0 0 1.1 x 2 = 1.1 in binary = 1.5 in decimal x 2 = 1.5 x 1 = 1.5 Adding 1 to an exponent (in binary) ..... x 2 Adding 1 to an exponent (in decimal) ..... x 10 1 1.1 x 2 = 1.1 x 2 = 3 in decimal 2 1.1 x 2 = 1.1 x 4 = 6 in decimal 3 1.1 x 2 = 12 in decimal 4 1.1 x 2 = 24 in decimal ---- 1 => move point forward 1 place if you want to express it as a normal number. 1.1 x 2 = 11 (base2) = decimal? 3 2 1.1 x 2 = move point forward 2 places = 110 (base 2) = decimal? 6 3 1.1 x 2 = move point forward 3 places = 1100 = 12 1100 (. is implied) --------------------------------------------- Example --------------------------------------------- 6 1.1 x 2 = decimal ? 6 1.1 x 2 = decimal ? Firstly, move point forward 6 places. 11 (1 place forward) 110 (2 places forward) 1100 (3 places forward) 11000 (4 places forward) 110000 (5 places forward) 1100000 (6 places forward) 1100000 (6 places forward) 1 1 0 0 0 0 0 64 32 16 8 4 2 1 1x0 = 0 2x0 = 0 4x0 = 0 8x0 = 0 16x0 = 0 32x1 = 32 64x1 = 64+ --- 96 6 1.1 x 2 = 1100000 = 96 decimal --------------------------------------------- End of Example ---------------------------------------------