Micrcontrollers

Micrcontrollers

Logic 0 and 1:
It has two possible states either 1 or 0. One of the region is represented by a logic state 'true' or 1 or 'high' or 'yes' state. The other region is represented by a logic state 'false' or 0 or 'low' or 'no' state.

Representation in the Number System:
A number can be represented by a set of logic state. For example, consider a set of 8-logic state ins 8 circuits giving the logic output = 0000 0000 can be represented by decimal 0, 0000 0001 can be represented by decimal 1,   0000 0010 can be represented by decimal 2... and so on. The 1111 1111 can represent decimal 255.

•  Binary Number: A binary number is a number which is based upon two value 0 and 1. Suppose there are 12 apples. How can we represent 12 in binary system so that the electronic circuits can be used for representing the 1s an 0s? One is that take one for each apple and write the 1s -111111111111 12 times. Alternately and efficient way is a follows: Consider a 4-bit number. The easier way is write 1 at the rightmost position, 1 at the left to the rightmost position and 0 at the leftmost but one and 0 at the leftmost position and assume the weight(w) of the left side digit is always two times (w_d=2_d) compared to the neighboring one of the right side. The binary number for decimal 12 is thus represented by 1100_b as 1100_b = 1 X (w_d)³ + 1 X (w_d)² + 0 X (w_d)¹ + 0 X (w_d)⁰ when w_d = 2
•  Decimal Number: A decimal number is a number based upon ten values:0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Suppose there are 12 apples. How can we represent 12 in a decimal system? Decimal representation way is write 2 at the rightmost position, 1 at the left of 2 and assume that the weight (w_d) of the left side digit is always ten times (w_d = 10) compare to the neighboring one on the right side. Decimal number one hundred is represented by 100 as a decimal 100d =  1 X (w_d)³ + 0 X (w_d)¹ + 0 X (w_d)⁰ when w_d = 10 d
• Conversion between binary and Decimal Number :  Conversion to decimal is required so that humans understand a number easily. Conversion to binary is required so that electronic circuits can perform the operation on the numbers. We can learn conversion with the following examples of the results of conversion. 
• Hexadecimal Numbers: A hexadecimal number is a number based upon 16 values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. A set of four binary bits is called one nibble, and a set of eight binary bits(two nibbles) is called one byte. Two hexadecimal together represent a byte.