Question

In the binary number system which is used in computer operations, there are only two digits allowed: 0 and 1.
A binary code is a system of binary numbers with a fixed number of digits that are used to represent letters, numbers, and symbols. To produce enough binary numbers to represent all of the letters of our alphabet (both upper and lower case), how many binary digits must be used?

Answer 1

There are 26 upper case letters
and
26 lower case letters in the alphabet

wouldn't the sum of those be enough binary numbers...?

Answer 2

like i could be wrong and not know enough about binary numbers

Answer 3

say we wanted to represent 1,2,3 are binary numbers
they would all 3 be different binary numbers but there would only be 3 because we only need to represent 3 digits

Answer 4

for example
1=01
2=10
3=11

Answer 5

we have 3 different binary numbers for the three different digits we wanted to represent as binary numbers

Answer 6

it says at the back of the book that the answer is "at least 6".. and I just wanted to know why 6?

Answer 7

oh! i understand what they are asking

Answer 8

like 1 through 3 can be represented by two digits
like 1=01
2=10
3=11
we needed 2 binary digits

Answer 9

so we need 26+26=54
i wonder what we would get if we tried to represent 54 in binary

Answer 10

ohkay? lol wait.. i'm really confused O.o

Answer 11

pretend we took the numbers 1 through 3 and we converted them to binary

Answer 12

we only need two base two place values
2^0 and 2^1

Answer 13

okkkaayyy?

Answer 14

do you understand that part?

Answer 15

why 2^0?

Answer 16

binary is based two

Answer 17

\[1_{10}=0 \cdot 2^1+1 \cdot 2^0=01_2 \\ 2_{10}=1 \cdot 2^1 +0\cdot 2^0=10_2 \\ 3_{10}=1 \cdot 2^1+1\cdot 2^0=11_2\]

Answer 18

so all you have to do is take the highest number in your set to figure out how many binary digits you will need for that set

Answer 19

take the highest number in your set and write it in binary

Answer 20

so 54 is the highest in our set

Answer 21

convert that number to binary

Answer 22

jee i don't know how to add
26+26=52

Answer 23

26+26=52 not 54 though? O.o

Answer 24

so 52 is the highest
convert that to binary

Answer 25

it was a type-o

Answer 26

you can add for me lol

Answer 27

lol you type too fast.. can you do it slowly?

Answer 28

this is what i understand so far ..

you said let's pretend that we took numbers 1, 2, &3
so since only 1 & 0 can be used as binary numbers.....
we have to...

Answer 29

brb, dinner..

Answer 30

when we converted 3 to binary number 11
we seen that we only needed two digits for each number from 1 to 3

if we had {1,2,3,4,5,6,7,8,9,10}
10=1*2^3+0*2^2+1*2^1+0^2^0
so we only need 4 binary place values
the one's digit, the two's digit, the four's digit, the eight's digit