Chapter1 - EE2006 Digital Design/S Ranganath I. Number...

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EE2006 Digital Design/S Ranganath I - 1 I. Number Systems Basic binary addition, subtraction and multiplication. Positional number systems ± Binary, octal, decimal, hexadecimal. Conversions between number systems. Signed binary number representations. ± Signed magnitude, One’s complement, Two’s complement. Signed binary addition and subtraction. Binary coded decimal (BCD) representation. 4 number systems that we must be familiar with: System Why? Remarks Decimal 10 fingers Binary ON/OFF systems 3 times more digits than decimal Octal Shorthand notation for working with binary 3 times less digits than binary Hex ------- do --------- 4 times less digits than binary
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EE2006 Digital Design/S Ranganath I - 2 Binary Addition a + b : Truth Table a b sum carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 +1 +1 2 (wrong!) 1 0 (sum = 0, carry = 1) Examples: 1. 1 1 0 6 1 1 3 1 1 1 7 1 0 0 0 0 16 2. 1 1 0 1 1 . 1 0 1 27.625 1 0 1 0 . 1 1 1 10.875 1 0 0 1 1 0 . 1 0 0 38.5 Note: Addition rule for binary non-integers same as for integers.
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EE2006 Digital Design/S Ranganath I - 3 Binary Subtraction a - b a: minuend b: subtrahend Truth Table a b Difference Borrow 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 Examples: 1. 1 1 1 0 14 - 1 0 0 - 4 1 0 1 0 10 2. 1 1 0 1 13 - 1 0 - 2 1 0 1 1 11 3. 1 1 0 0 0 1 49 - 1 0 0 1 1 - 19 1 1 1 1 0 30 Note: Subtraction rule for binary non-integers same as for integers
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EE2006 Digital Design/S Ranganath I - 4 Binary multiplication a x b Truth Table a b Product 0 0 0 0 1 0 1 0 0 1 1 1 Example: 1 1 0 1 . 1 x 1 0 1 0 . 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 .1 1 Note: Rule for positioning binary point identical to that in decimal number system.
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EE2006 Digital Design/S Ranganath I - 5 Positional Number Systems Have a radix (base) associated with them. In the decimal system, r = 10, and there are 10 symbols, 0 - 9.
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This note was uploaded on 08/02/2009 for the course ECE EE2006 taught by Professor Dr.kassim during the Fall '07 term at National University of Singapore.

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Chapter1 - EE2006 Digital Design/S Ranganath I. Number...

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