The binary number system is also called base 2. This is because it only offers the possibility of using two numerals to describe an amount.
Binary numbers are made of 0's and 1's.
A computer understands bits.
A bit in our computer language is defined as one binary digit.
A binary digit represents a measurement of a thing. Each digit has only two possibilities: 0 or 1.
Each binary digit is made from Character data composed of letters, symbols, and numerals that are not used in arithmetic operations, such as your name, address or your hair color.
Just like Morse code uses dashes and dots to represent letters of the alphabet, computers use a series of bits to represent letters, numerals and other characters.
Digital devices employ several types of code to represent character data, such as ASCII, EBCDIC, and Unicode.
The codes follow protocol using the binary number system also understood by the computers.
The Decimal numbers system uses 10 symbols to represent numbers: 0,1,2,3,4,5,6,7,8,9.
The binary system like mentioned above uses only two symbols 0 and 1.
A formula that explains how to convert
Decimal numbers into Binary numbers:
Binary numbers are read a byte at a time and one byte equals to eight bits.
Decimal numbers into Binary numbers:
Binary numbers are read a byte at a time and one byte equals to eight bits.
Start with 8 digits to represent a binary number (byte).
Binary stands for bi which stands for 2. (base2)
2°=1Binary stands for bi which stands for 2. (base2)
2¹=2
2²=4
2³=8 and so forth to the 7th power.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 |
No it cannot so I added a 0 (zero) under the 128 (8th digit)
Can you fit 64 into the number 54?
No it cannot, so I placed a 0 under the 7th digit (64)
Can 32 fit into 54?
Yes so I placed a 1 (one) under the 6th digit (32)
64-32=22
Can you fit 16 into 22?
Yes so I placed a 1 under the 5th digit (16)
22-16=6
Can you fit 8 into 6?
No, so I added a 0 under the 4th digit (8)
Can you fit 4 into 6?
Yes, so I place a 1 under the 3rd digit (4)
6-4=2
Can I fit 2 into 2?
Yes, added a 1 under the 2nd digit (2)
2-2=0
Can I fit 1 into 0?
No, so I added a 0 to the 1st digit (1)
The zeros before the first 1 can be removed.
The decimal number 54 converts to binary 110110.
More examples are shown in the tables below.
Decimal Number | Binary Number |
8 | 1000 |
25 | 11001 |
136 | 10001000 |
1492 | 10111010100 |
Decimal Number | Binary Number |
25 | 11001 |
26 | 11010 |
27 | 11011 |
28 | 11100 |
29 | 11101 |
30 | 11110 |
"There are only 10 types of people in the world: Those who understand binary and those who don't."
If you see a group of individuals wearing the T-shirt "There are only 10 types of people in the world: Those who understand binary and those who don't"
You will only wonder where to get your own awesome T-shirt like that, because in binary we all know that 1 and 0 is 2. And it looks like decimal #10 to the type of people who do not know binary.
The binary number system is used by all computers. The binary number system has only two numbers, 0 and 1, called binary digits, or bits.
ReplyDeleteIn a computer all counting and calculations use the binary system.
All letters and numbers are stored in a computer as a series of bits, each represented in the computer as on or off. (zero is off and one is on).
Because of the way the number system is organized, grouping is often done in groups of eight bits, each of which is called a byte.
( eight bits = one byte)
The most common coding method for text is ASCII ( American Standard Code for Information Interchange). for example, the upper case letter "A" in ASCII code is 0100 0001.
All communication, storage, and processing of data inside a computer are in binary form until presented as output to the user.
Counting in binary goes like this: 0,1,10,11,100,101,110,111 and so on........
Binary code for the number 25 equals 0001 1001 ( The number 25 stored as 8 bits using the binary number system).
A simple solution to figure binary code for numbers is to divide by 2:
for our example #25 we divide 25 by 2 to get 12 with a remainder of 1. ( use the remainder to create the binary code, starting from the right and working to the left). Now we take 12 divide by 2 which equals 6 with a remainder of 0 (zero). Now we take 6 divided by 2 and get 3 with a remainder of 0. Then 3 divided by 2 equals 1 remainder 1. Then we divide 1 by 2 and get 0 remainder of 1.
Since we use 8 bits to create out binary code we must create 8 digits. (Remember that we used the remainders and placed them right to left). The formula we just used offers 5 digits and we need 8, so we add 3 zeros left of the other 5 to create our binary code for the number 25 = 00011001.( This binary code has 128 bits) (from right to left 1,2,4,8,16,32,64,128)