Let's approach this by seeing how to convert any hexadecimal number into binary. As you should know, a single hex digit is equal to 4 binary digits. Since one hex digit can count as high as fifteen (0 - F) and it takes 4 binary digits to count to fifteen (0000 - 1111) then 4 binary bits are needed to represent a single hex digit. Now look how easy it is to convert any size hex number into binary:
Take this four digit hex number: 9BF8. All you have to do is convert each hex digit into it's 4 bit binary representation like so:
...9......B.....F......8....
1001 1011 1111 1000
So 9BF8 = 1001011111111000
And of course, you can do just the opposite to convert binary to hex:
1001 1011 1111 1000
...9......B.....F......8....
Now let's look at how you work four binary digits. The place values for binary increase 2 times every time you move to the left like so:
8 4 2 1
0 0 0 0 = 0 + 0 + 0 + 0 = 0
0 0 0 1 = 0 + 0 + 0 + 1 = 1
0 0 1 0 = 0 + 0 + 2 + 0 = 2
0 0 1 1 = 0 + 0 + 2 + 1 = 3
0 1 0 0 = 0 + 4 + 0 + 0 = 4
0 1 0 1 = 0 + 4 + 0 + 1 = 5
0 1 1 0 = 0 + 4 + 2 + 0 = 6
0 1 1 1 = 0 + 4 + 2 + 1 = 7
1 0 0 0 = 8 + 0 + 0 + 0 = 8
1 0 0 1 = 8 + 0 + 0 + 1 = 9
. . . . .
. . . . .
. . . . .
1 1 1 1 = 8 + 4 + 2 + 1 = 15
A hexadecimal digit is one number in a "Base 16" set, represented by the Base 10 digits of 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F, where 0 is 0 and F is 15. In order to represent the number 16, you need to have two digits. (10 represents 16)
A Binary digit is one number in "Base 2", represented by the base 10 digits of 0 and 1.
Therefore, the Hex number F (15) is represented by the binary number 1111 (15)
4 binary digits are needed to represent 1 hexadecimal digit.
0 - 0000
1 - 0001
2 - 0010
3 - 0011
4 - 0100
5 - 0101
6 - 0110
7 - 0111
8 - 1000
9 - 1001
A - 1010
B - 1011
C - 1100
D - 1101
E - 1110
F - 1111
4
as you know hex goes 1 2 3 4 5 6 7 8 9 a b c d e f
which is equivalent to 15 (in decimal)
S0 15 in Binary is 1111
Your question is poorly phrased. zero is a hexadecimal digit, and is represented
by one binary digit, 0. One is also a hex digit, and is represented by one binary
digit, 1. hex 2 is 10, so takes two binary digits. In general, a hex digit takes at most 4 binary digits, and at least 1. There is one correct answer and one favorite answer. Then there is Eddie's answer, and AJ's answer, and Phillip's answer.
>
> John (gnujohn)
4
1111 binary = 15 decimal = F hex
