Binary numbers ?

Question

I am really confused about binary numbers, could someone help me with this question please. If a binary number needs to represent 16 different values, how long must the number be in bits ?

Answer 1

In base 10 numbering systems, there are 10 different nubmers we use, 0-9. When we get to 9, the next number is 10, and so forth. Binary numbers only have 2 different numbers, 0 and 1. So the first binary number, 0, would be 0 in base 10. 1 in binary is just 1. 2 in binary is 10, since there are no other numbers to use. 3 in binary is 11, 4 is 100. You see the pattern arising here. All powers of 2 are represented as 1 followed by some number of 0's. So in order to find out what 16 is you need to figure out how many powers of 2 are in 16 starting from 1 and doubling , in this case 5. 1,2,4,8,16. So in order to express all possible numbers up to 16 in binary form you need to have binary number 16 as 10000. With that you can espress all the numbers from 0 to 16.

Answer 2

binary no 128/64/32/16/8/4/2/1/ binary language is the language of computer you want the value of 16
128/64/32/16/8/4/2/1/=binary table
0 0 0 1 0 0 0 0 when the given no. is greater than on the binary table write 1 when the given no. is less than write 0


16=00010000

Answer 3

In decimal numbers, there are ten possible numbers in each position (0,1,2,3,4,5,6,7,8,9). Within a decimal number with more than one digit, the rightmost digit represents the "ones" position. The second position from the right represents "tens." The third position from the right represents "hundreds," etc. Each position represents TEN times the number in the position to its right.

Binary numbers are similar. With binary numbers there are two possible digits in each position in the number. In the binary system these numbers are 0 and 1. The rightmost position in a number with more than one digit represents the "ones." The second position from the right represents the "twos." The third position represents the "fours." The fourth position represents the "eights." etc. Each position represents TWO times the number in he position to its right.

Compare:

(Ten thousands) (thousands) (hundreds) (tens) (ones)
(sixteens) (eights) (fours) (twos) (ones)

A decimal number with 3 digits can represent one thousand values... 001 to 999 plus the number 0. So, the number of values you represent is one more than the the maximum number if all the positions are filled with the highest numeral.

To represent 16 different values, you need to be able to count from 0 to 15 (in decimal speak).

So, comparing it with the decimal system, you would have:

decimal ----- binary ----- (looking at each position in the binary number)
00 ----- 0000 ----- (0x8 + 0x4 + 0x2 + 0) ----- first value
01 ----- 0001 ----- (0x8 + 0x4 + 0x2 + 1) ----- second value
02 ----- 0010 ----- (0x8 + 0x4 + 1x2 + 0) ----- third value
03 ----- 0011 ----- (0x8 + 0x4 + 1x2 + 1) ----- fourth value
04 ----- 0100 ----- (0x8 + 1x4 + 0x2 + 0) ----- fifth value
05 ----- 0101 ----- (0x8 + 1x4 + 0x2 + 1) ----- sixth value
06 ----- 0110 ----- (0x8 + 1x4 + 1x2 + 0) ----- seventh value
07 ----- 0111 ----- (0x8 + 1x4 + 1x2 + 1) ----- eighth value
08 ----- 1000 ----- (1x8 + 0x4 + 0x2 + 0) ----- ninth value
09 ----- 1001 ----- (1x8 + 0x4 + 0x2 + 1) ----- tenth value
10 ----- 1010 ----- (1x8 + 0x4 + 1x2 + 0) ----- eleventh value
11 ----- 1011 ----- (1x8 + 0x4 + 1x2 + 1) ----- twelfth value
12 ----- 1100 ----- (1x8 + 1x4 + 0x2 + 0) ----- thirteenth value
13 ----- 1101 ----- (1x8 + 1x4 + 0x2 + 1) ----- fourteenth value
14 ----- 1110 ----- (1x8 + 1x4 + 1x2 + 0) ----- fifteenth value
15 ----- 1111 ----- (1x8 + 1x4 + 1x2 + 1) ----- sixteenth value
16 ----- 10000 ----- (1x16 + 0x8 + 0x4 + 0x2 + 0) ----- eventeenth value

Please note that this table represents numbers that are both whole and positive.

So, in order to count to 16 in binary, you need a number that is five digits long. BUT, in order to represent sixteen values, you only need a number that is 4 digits long because zero counts as a value.

One other "bit" of binary trivia (pun intended): In binary, each digit in a multidigit number is sometimes termed a "bit." Thus a four digit binary number has four bits.

Answer 4

http://www.google.com/search?q=Binary+numbers

Answer 5

There are 8 bytes in a bit. That's 2 bits.