Louis Braille devised a system of six raised or not-raised dots to signify a letter of the alphabet.
a) How many different letters or characters may be coded in Braille?
b) If you wanted to code 94 distinct characters, such as those found on a computer keyboard, how mant dots would the system need?
a) In the Braille system, there are 6 dots arranged in 2 columns and 3 rows. To determine the number of different characters that can be coded in Braille, we need to find out how many different combinations of these dots are possible.
Each dot can either be raised or not raised, giving us 2 possibilities for each dot. Since there are 6 dots in total, we can calculate the number of possible combinations using the formula for permutations:
Number of combinations = 2^6 = 64
Therefore, the Braille system can code 64 different letters or characters.
b) If you wanted to code 94 distinct characters, such as those found on a computer keyboard, we need to determine how many dots the system would need.
Since we already know that the Braille system can code 64 different characters, we need to find the minimum number of additional dots required to reach 94.
One way to do this is to calculate the smallest power of 2 that is greater than or equal to 94. We can do this by finding the logarithm base 2 of 94 and rounding up to the next integer:
Number of additional dots = ceil(log2(94)) = ceil(6.554588851677638) = 7
Therefore, in order to code 94 distinct characters, the Braille system would need 7 additional dots, making a total of 13 dots (6 original dots + 7 additional dots).