Number System in Digital Design

To represent something we require symbols and to represent count we require Numbers. Number System is very important in Digital Technology. The most commonly used number systems are Decimal(Base 10), Binary(Base 2), Hexadecimal(Base 16) and Octal(Base 8). We all are very much familiar with Decimal Number System.

• Decimal Number System
• It is composed of 10 symbols.
• These are 0,1,2,3,4,5,6,7,8 and 9.
• It is also called as Base-10 Number System because there are 10 symbols.
• Examples are 791.990, 1491994, 511
• 791.990 = (7*10^2) + (9*10^1) + (1*10^0) + (9*10^-1) + (9*10^-2) + (0*10^-3) 
• Binary Number System
• It is composed of only 2 symbols.
• These are 0 and 1.
• Examples are 1010, 1110, 11001010.
• 1010 = (1*2^3) + (0*2^2) + (1*2^1) + (0*2^0) = 10 in Decimal Number System.
• In 11001010 example, leftmost four bits(1100) is called as MSB(Most Significant Bits) and rightmost four bits(1010) is called as LSB(Lower Significant Bits).
• Group of 4 bits is called as Nibble, 8 bits is called as Byte, 16 bits is called as Word.
• Hexadecimal Number System
• It uses base 16.
• It has 16 symbols.
• These are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.
• Examples are 1010, 111A, ABCD123,1265.ADC.
• 1010 = (1*16^3) + (0*16^2) + (1*16^1) + (0*16^0) = 4112 in Decimal Number System.
• Octal Number System
• It is composed of 8 symbols.
• These are 0,1,2,3,4,5,6 and 7.
• Examples are 126, 75.63, 563524.
• 126 = (1*8^2) + (2*8^1) + (6*8^0) = 86 in Decimal Number System.