Electrical Engineering ⇒ Topic : Binary Number System

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BINARY NUMBER SYSTEM It uses only two digits, 0 and 1. The base or radix of the binary number system is 2. A binary digit is called a bit. The digital computer stores data in terms of 0 and 1. The output of such an element at any time is either high (1 volt) or low (0 volt). There is no other stable state except these two stable states. The two stable states can be represented by 0 and 1, respectively, that is low is represented by 0 and high is represented by 1. There is no difficulty to represent numbers up to 9 in decimal number system. There is no digit to represent ten. Therefore, it is represented by 10 utilizing positional technique. Similarly,utilizing positional techniques hundred is represented by 100. In binary number system, zero is represented by 0 and one by 1. There is no digit to represent two. It is written as 10 utilizing positional technique. Three and four are written as 11 and 100, respectively. The weight of each binary bit of a binary number depends on its relative position within the number. To explain this,let us take a binary number 1011. (1011)_{2} = 1 x 2^{3}+0 x 2^{4}+1 x 2 +l x 2° = 8 + 0 + 2 + 1 = (11)_{10} Therefore, the weight of each bit of binary number depends on its relative position within the number, i.e., Weight of the 1st bit of the binary number from the right hand side = 1st bit x 2° Weight of the 2nd bit of the binary number from the right hand side = 2nd bit x 2^{1} Weight of the 3rd bit of the binary number from the right hand side = 3rd bit x 2^{2} Weight of the 4th bit of the binary number from the right hand side = 4th bit x 2^{3} Weight of the nth bit = nth bit x 2^{n1} = nth bit x (base)^{n1}  
 
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