NumberRepresentation-1

# NumberRepresentation-1 - Kingdom Of Saudi Arabia Al-Imam...

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Number Representation Chapter 3 in “Foundation of Computer System” Kingdom Of Saudi Arabia Al-Imam Muhammad Ibn Saud Islamic University College of Computer and Information Sciences Information System Department 1 st semester, 2010 – 2011 CS 224: Computer Organization 1 T. Hala A. Al-Rumaih

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Decimal and binary Two numbering systems are dominant today in the world of computers: 2
Decimal System We all readily understand the decimal numbering system. But is it really under stand: Why the second position in the decimal system is tens and the third position is hundreds? The answer lies in the powers of the base (weight) of the system. The base in the decimal system is = 10. The first position is raised to the power 0 The second position is raised to the power 1 The third position is raised to the power 3 3

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Decimal System (Cont.) 4
Binary system Whereas the decimal system is based on 10 , the binary system is based on 2 . There are only two digits in the binary system 0 and 1 . 5

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Conversion Binary to Decimal Conversion: 1. Start with binary number and multiply each binary digit by its weight ( Base 2 ) Since each binary bit can be only 0 or 1 the result will be either 0 or the value of the weight. 1. After multiplying all the digits, add the results. 6
Conversion (Cont.) EX: Convert the binary number 10011 to decimal. Write out the bits and their weights. Multiply the bit by its corresponding weight and record the result. At the end, add the results to get the decimal number. 7

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(Cont.) Decimal to Binary Conversion: 1. Repeatedly division by 2 , the process continues until the quotient is 0 2. The result will be the remainder of the division ( 0 or 1 ) take it from up to down, write it from right to left. 8
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NumberRepresentation-1 - Kingdom Of Saudi Arabia Al-Imam...

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