Computer Science XI

Binary Number System

Ten different digits 0 – 9 are used to represent numbers in the decimal system. There are only two digits in the binary system, namely, 0 and 1. The numbers in the binary system are represented to the base two and the positional multipliers are the powers of two. The leftmost bit in the binary number is called as the most significant bit (MSB) and it has the largest positional weight. The rightmost bit is the least significant bit (LSB) and has the smallest positional weight. The binary sequence 101112 has the decimal equivalent: 1011112 = 1 x 24 + 0 x 23 + 1 x 22 + 1 x 21 + 1 x 21 + 1 x 20 = 16 + 0 + 4 + 2 + 1 = 2310
21
The decimal equivalent of the fractional binary sequence can be estimated in the same manner. The exponents are negative powers of two for digits on the right side of the binary point. The binary equivalent of the decimal point is the binary point. Thus the decimal value of the fractional binary sequence 0.10112 is: 0.10112 = 1 x 2–1 + 0 x 2–2 + 1 x 2–3 + 1 x 2–4 = 0.5 + 0 + 0.125 + 0.0625 = 0.687510

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