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01S Number Systems

# 01S Number Systems - EE2000 Logic Circuit Design 1 Number...

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1 EE2000 Logic Circuit Design 1 (Supplementary Notes) ±

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2 Binary Addition: 2 nd Example ± Compute the sum of (1101) 2 and (0101) 2 ± (1101) 2 = (13) 10 , (0101) 2 = (5) 10 ± Result is correct (10010) 2 = (18) 10 , but… 1 1 0 1 0 1 0 1 +) 0 Carries Augend Addend Sum 1 0 0 1 0 1 0 1 1
3 But … ± Addition of two 4-bit number may produce a 5-bit number ± OK for mathematics, but may not for computer systems ± For computer system, the extra carry out bit will be ignored ± i.e. for a 4-bit system, input two nos. are 4- bit, the output must also be 4-bit

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4 Look at Previous Example Again ± The actual output of the system is (0010) 2 ± = 2 10 ± Result incorrect! ± The phenomenon is called overflow 1 1 0 1 0 1 0 1 +) 1 0 0 1 0 1 1 0 1 0 0 0 1 0 2 = 2 10 1 0 0 1 0 2 = 18 10
5 Overflow ± There is a limitation in addition for computer system ± e.g. ± For 4-bit binary system ± The range of sum is 0 sum 15 ± Overflow when sum < 0, or sum > 15 ± For 4-bit 2’s complement binary system ± The range of sum is -8 sum +7 ± Overflow when sum < -8, or sum > 7

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01S Number Systems - EE2000 Logic Circuit Design 1 Number...

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