1. Have you ever asked yourself why do human beings choose the decimal number system?
Well, some people believe that it’s because we have 10 fingers! You see that the humans started counting when they felt the need to do so. Probably to count the number of cattle in their herd in order to ensure that they were all there! Now put yourself in place of a nomad who does not know how to count. How will you do so? You will probably use a nearest tool! The best tool in this scene would be your hands! You assign a finger to each cattle you see and count. Now since you have 10 fingers, you go back and start counting from the beginning again, thus making sets of 10! This is where the concept of using 10 numbers (base 10) or decimal number system evolves!
2. Why do computers use binary?
There are many advantages to binary. Here are four (somewhat overlapping) important reasons for using binary:
- Binary devices are Simple and easy to build.
- Binary signals are Unambiguous (which gives them noise immunity).
- Flawless copies can be made of binary data.
- Anything that can be represented with some sort of pattern can be represented with patterns of bits.
3. What is the Binary Number System?
Binary numbers are made of 0s and 1s. It’s also called base 2 number system. Imagine aliens with two hands and one finger on each hand, and imagine the aliens have to count their alien cattle! They assign a finger to each cattle they see and count, once the number reaches 2, they go back and start counting from the beginning again, thus making sets of 2 instead of 10!
1 (base 2) = 1 (base 10) = 2^0
10 (base 2) = 2 (base 10) = 2^1
100 (base 2) = 4 (base 10) = 2^2
1000 (base 2) = 8 (base 10) = 2^3
10000 (base 2) =16(base 10) = 2^4
Now we can see that in the binary number system, 1 + 1 = 10!
Let’s check out a few more examples of binary addition!
10 + 1 = 11
11 + 1 = 100
101 + 1 = 110
Challenge: In the binary number system, what is the result of 101011 + 110111?
4. How to convert binary to decimal?
The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
decimal = d0×20 + d1×21 + d2×22 + …
Example #1
Find the decimal value of 1110012:
| binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
|---|---|---|---|---|---|---|
| power of 2: | 25 | 24 | 23 | 22 | 21 | 20 |
1110012 = 1⋅25+1⋅24+1⋅23+0⋅22+0⋅21+1⋅20 = 5710
Example #2
Find the decimal value of 1000112:
| binary number: | 1 | 0 | 0 | 0 | 1 | 1 |
|---|---|---|---|---|---|---|
| power of 2: | 25 | 24 | 23 | 22 | 21 | 20 |
1000112 = 1⋅25+0⋅24+0⋅23+0⋅22+1⋅21+1⋅20 = 3510