Let's go to computer basics. Have you ever thought how computer works? How the information is stored on the computer? Have you heard about bits and bytes? What are bits and bytes? I mentioned bits when I wrote about data types. Let's explore more about bit and its significance -
Bits - Bit is short form of binary digit. Like decimal digits are 0-9, binary digits (bits) are only two digits - 0 and 1. And you will be surprised to know that all informations stored in digital form is represented by bits only. A bit is the smallest unit of information on a machine. In decimal digits, we have base 10 counting. In binary digits, we use base 2 counting. By combining bits you can obtain larger units. In decimal digits, we have base 10 counting. For example: 32-bit addresses, 64-bit addresses, 1-bit image (monochrome), 8-bit image (256 colors / grayscales) and 24- or 32-bit graphics. You can have so many examples of bits.
Nibbles - Combination of 4 bits is called a nibble. In binary counting, we can have any number of digits, but only in 0s and 1s. Nibble values have range from 0 (0000) to 15 (1111). See the following chart, how we can convert binary values into decimal.
Bytes - Combination of 8 bits is called a byte. A byte can have values from 0 (0000 00000) to 255 (1111 1111). Let's see what value is for 1010 0101
Value for Byte 1010 0101 is = 128 + 32 + 4 + 1 = 165
How to convert decimal to binary value?
To convert decimal value to the binary value (bits), we should divide the number successively by 2 and get the remainders as 0s and 1s. Let's see an example here, converting 237 into binary value :
So, binary value for the number 237 is 1110 1101. Let's confirm this -
128 + 64 + 2 + 1 = 195
Bits - Bit is short form of binary digit. Like decimal digits are 0-9, binary digits (bits) are only two digits - 0 and 1. And you will be surprised to know that all informations stored in digital form is represented by bits only. A bit is the smallest unit of information on a machine. In decimal digits, we have base 10 counting. In binary digits, we use base 2 counting. By combining bits you can obtain larger units. In decimal digits, we have base 10 counting. For example: 32-bit addresses, 64-bit addresses, 1-bit image (monochrome), 8-bit image (256 colors / grayscales) and 24- or 32-bit graphics. You can have so many examples of bits.
Nibbles - Combination of 4 bits is called a nibble. In binary counting, we can have any number of digits, but only in 0s and 1s. Nibble values have range from 0 (0000) to 15 (1111). See the following chart, how we can convert binary values into decimal.
| Nibble | Convert To Decimal | Evaluate | Value |
|---|---|---|---|
| 0000 | 0 X 23 + 0 x 22 + 0 x 21 + 0 x 20 | 0 + 0 + 0 + 0 | 0 |
| 0001 | 0 X 23 + 0 x 22 + 0 x 21 + 1 x 20 | 0 + 0 + 0 + 1 | 1 |
| 0010 | 0 X 23 + 0 x 22 + 1 x 21 + 0 x 20 | 0 + 0 + 2 + 0 | 2 |
| 0011 | 0 X 23 + 0 x 22 + 1 x 21 + 1 x 20 | 0 + 0 + 2 + 1 | 3 |
| 0100 | 0 X 23 + 1 x 22 + 0 x 21 + 0 x 20 | 0 + 4 + 0 + 0 | 4 |
| 0101 | 0 X 23 + 1 x 22 + 0 x 21 + 1 x 20 | 0 + 4 + 0 + 1 | 5 |
| 0110 | 0 X 23 + 1 x 22 + 1 x 21 + 1 x 20 | 0 + 4 + 2 + 0 | 6 |
| 0111 | 0 X 23 + 1 x 22 + 1 x 21 + 1 x 20 | 0 + 4 + 2 + 1 | 7 |
| 1000 | 1 X 23 + 0 x 22 + 0 x 21 + 0 x 20 | 8 + 0 + 0 + 0 | 8 |
| 1001 | 1 X 23 + 0 x 22 + 0 x 21 + 1 x 20 | 8 + 0 + 0 + 1 | 9 |
| 1010 | 1 X 23 + 0 x 22 + 1 x 21 + 0 x 20 | 8 + 0 + 2 + 0 | 10 |
| 1011 | 1 X 23 + 0 x 22 + 1 x 21 + 1 x 20 | 8 + 0 + 2 + 1 | 11 |
| 1100 | 1 X 23 + 1 x 22 + 0 x 21 + 0 x 20 | 8 + 4 + 0 + 0 | 12 |
| 1101 | 1 X 23 + 1 x 22 + 0 x 21 + 1 x 20 | 8 + 4 + 0 + 1 | 13 |
| 1110 | 1 X 23 + 1 x 22 + 1 x 21 + 0 x 20 | 8 + 4 + 2 + 0 | 14 |
| 1111 | 1 X 23 + 1 x 22 + 1 x 21 + 1 x 20 | 8 + 4 + 2 + 1 | 15 |
Bytes - Combination of 8 bits is called a byte. A byte can have values from 0 (0000 00000) to 255 (1111 1111). Let's see what value is for 1010 0101
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
|---|---|---|---|---|---|---|---|
| 1 x 27 | 0 x 26 | 1 x 25 | 0 x 24 | 0 x 23 | 1 x 22 | 0 x 21 | 1 x 20 |
| 128 | 0 | 32 | 0 | 0 | 4 | 0 | 1 |
Value for Byte 1010 0101 is = 128 + 32 + 4 + 1 = 165
How to convert decimal to binary value?
To convert decimal value to the binary value (bits), we should divide the number successively by 2 and get the remainders as 0s and 1s. Let's see an example here, converting 237 into binary value :
| Divide by 2 | Quotient | Remainder | 2 to the power |
|---|---|---|---|
| 237 / 2 | 118 | 1 | 20 |
| 118 / 2 | 59 | 0 | 21 |
| 59 / 2 | 29 | 1 | 22 |
| 29 / 2 | 14 | 1 | 23 |
| 14 / 2 | 7 | 0 | 24 |
| 7 / 2 | 3 | 1 | 25 |
| 3 / 2 | 1 | 1 | 26 |
| 1 / 2 | 0 | 1 | 27 |
So, binary value for the number 237 is 1110 1101. Let's confirm this -
| 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
|---|---|---|---|---|---|---|---|
| 1 x 27 | 0 x 26 | 1 x 25 | 1 x 24 | 0 x 23 | 1 x 22 | 0 x 21 | 1 x 20 |
| 128 | 64 | 32 | 0 | 8 | 4 | 0 | 1 |
128 + 64 + 32 + 8 + 4 + 1 = 237
Example 1: What is the binary value of decimal number 219?
Example 1: What is the binary value of decimal number 219?
Solution :
So, binary value for the number 219 is 1101 1011. Let's confirm this -
Example 2: What is the decimal value of binary value 1100 0011?
| Divide by 2 | Quotient | Remainder | 2 to the power |
|---|---|---|---|
| 219 / 2 | 109 | 1 | 20 |
| 109 / 2 | 54 | 1 | 21 |
| 54 / 2 | 27 | 0 | 22 |
| 27 / 2 | 13 | 1 | 23 |
| 13 / 2 | 6 | 1 | 24 |
| 6 / 2 | 3 | 0 | 25 |
| 3 / 2 | 1 | 1 | 26 |
| 1 / 2 | 0 | 1 | 27 |
So, binary value for the number 219 is 1101 1011. Let's confirm this -
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
|---|---|---|---|---|---|---|---|
| 1 x 27 | 1 x 26 | 0 x 25 | 1 x 24 | 1 x 23 | 0 x 22 | 1 x 21 | 1 x 20 |
| 128 | 64 | 0 | 16 | 8 | 0 | 2 | 1 |
128 + 64 + 16 + 8 + 2 + 1 = 219
Example 2: What is the decimal value of binary value 1100 0011?
Solution :
1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
|---|---|---|---|---|---|---|---|
1 x 27 | 1 x 26 | 0 x 25 | 0 x 24 | 0 x 23 | 0 x 22 | 1 x 21 | 1 x 20 |
128 | 64 | 0 | 0 | 0 | 0 | 2 | 1 |
128 + 64 + 2 + 1 = 195
No comments:
Post a Comment