Binary Numbers?

Question

If a binary number needs to represent 16 different values, how long must the number be in bits, am I right in thinking that it is 4 bits ?

the only answers i have got are, 1 bit- 2 bit- 3 bit- 4 bit 8 bit & 16 bits

Answer 1

If the smallest number is 0 and the largest 15, then four bits suffices (15 is 1111 in binary).

Answer 2

it should be 5 bits.
think in this fashion - to get binary 16 follow 16+8+4+2+1
to get binary 42 follow 32+16+8+4+2+1
42=32+0+8+0+2+0=(101010)

Answer 3

they are numbers written with in undemanding terms the digits one million and 0. See, we use what's stated as a base-10 numbering gadget, meaning that we've 10 digits--0, one million, 2, 3, 4, 5, 6, 7, 8, and nine. After nine, we initiate off making 2-digit numbers, which incorporate forty two. interior the extensive style forty two, the 1st digit is the ten's place, and the actuality that there is a 4 there capability that 10 is going into forty two 4 instances. the 2nd digit is the single million's place and the two there capability that when you have taken out each of the ten's, one million is going into forty two two times. So, ok, you found out all that throughout the time of preschool. what's it have been given to do with binary numbers? nicely, in a binary gadget, there are in undemanding terms 2 digits: 0 and one million. After one million, you may desire to initiate writing diverse-digit numbers. the placement at the back of the single million's place is the two's place, and at the back of it truly is the 4's place--powers of two extremely than powers of 10 like we are used to. case in point, forty two may well be written 101010 in binary. the 1st extensive style is interior the 32's place. a thank you to interpret it truly is that there is one 32, one 8 and one 2. (The sixteen,s, 4's, and one million's places have 0's in them.) upload 32, 8 and a pair of and additionally you get forty two. Binary is crucial because of the fact desktops use it. They perform via switches with in undemanding terms 2 positions--on and rancid--which correspond to 0 and one million in binary and permit them to checklist numbers.

Answer 4

At that level, you should be able to check this simply by writing down all the possibilities.

from that you should be able to derive a rule:

2 bits:
00
01
10
11
four possible values

3 bits:
000
001
...
110
111
Eight possible values

...
(try it for 4 bits)
...

General rule:

The total number of possible values =
2^(number of bits)

For example, with 10 bits, total number of possible values = 2^10 = 1024.

Answer 5

well on each possition there can be two values 0 and 1
let n be the number of positions
2*2*...*2 (n times) = 16
aka
2^n=16
n = 4