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Digital Literacy Computer Basics Computer Basics Binary

Sam Katz
Sam Katz
2,986 Points
Posted by Sam Katz
Sam Katz
2,986 Points

I understand that 00000011 is 3, but not why.

Thanks for explaining.

3 Answers

bothxp
bothxp
16,510 Points

Hi Sam,

I think of it like this:

Binary numbers are made up of 0s & 1s. From right to left the digit represent 1,2,4,8,16,32,64,128. If the bit is a 1 then you add the number that it represents.

| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|  0  |  0 |  0 |  0 | 0 | 0 | 1 | 1 |
=========================
  0 + 0 + 0 + 0 + 0 + 0 + 2  +  1

So 00000011 = 3

For another example:

| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|  0  |  1 |  0 |  0 | 0 | 0 | 1 | 1 |
=========================
  0 + 64 + 0 + 0 + 0 + 0 + 2  +  1

So 01000011 = 67

But where do the 1,2,4,8,16,32,64,128 numbers come from ?

If we start with our decimal system, then 235 can be split into Hundreds, Tens & Ones

| H | T | O |
| 2 | 3 | 5 |
= 235

Decimal works in base 10, so we can also write the above using 10^2 = 100, 10^1 = 10 & 10^0 = 1

| 10^2 | 10^1 | 10^0 |
|   2  |   3  |   5  |
= 235

The binary system operates in base 2, so we use:

2^7 = 2*2*2*2*2*2*2 = 128
2^6 = 2*2*2*2*2*2 = 64
2^5 = 2*2*2*2*2 = 32
2^4 = 2*2*2*2 = 16
2^3 = 2*2*2 = 8
2^2 = 2*2 = 4
2^1 = 2 = 2
2^0  = 1 

| 2^7  | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 |
| 128  |  64 |  32 |  16 |  8  |  4  |  2  |  1  |
Melanie Day
Melanie Day
5,540 Points

Great explanation :)

tracy
tracy
32,769 Points
tracy
tracy
32,769 Points

In binary numbers, the first digit (from right to left) represents 1, the second represents 2, then 4, 8, etc. So 00000011 has a "1" in the 1 column and "1" in the "2" column. Since 1 + 2 = 3, the answer is 3.

Does that help?

Sam Katz
Sam Katz
2,986 Points
Sam Katz
Sam Katz
2,986 Points

I appreciated all the answers. Binary is very relevant to both subnetting and computers in general. (although subnetting is base-16.)