EEM16_F13_L07 - EEM16/CSM51A Logic Design of Digital...

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EEM16/CSM51A: Logic Design of Digital Systems Lecture #7 Arithmetic Circuits Prof. Danijela Cabric Fall 2015
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2 (c) 2005 - 2012 W. J. Dally Numbers Digital logic works with binary numbers Each bit has a value based on its position
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3 (c) 2005 - 2012 W. J. Dally From Decimal To Binary Example: 17 10 Convert number to binary base: 17 ÷ 2 = 8 remainder 1 8 ÷ 2 = 4 remainder 0 4 ÷ 2 = 2 remainder 0 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 17 10 = 10001 2 MSB LSB
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4 (c) 2005 - 2012 W. J. Dally From Decimal To Binary To Hexadecimal Example: 1963 10 1963 10 = 0111 1010 1011 2 7 A B hex
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Binary addition 1-bit 0+0 = 0, 1+0 = 1, 1+1 = 10 1 6 110 + 3 011 5 101 +7 111 0 _ 10 01 001 110 1001 9 0 1 _ 00 11 100 111 1100 12 (c) 2005 - 2012 W. J. Dally
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6 (c) 2005 - 2012 W. J. Dally Half Adder HA a b c s b a c s
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7 (c) 2005 - 2012 W. J. Dally One bit of an adder Counts the number of “1” bits on its input Outputs the result in binary For a half-adder, 2 inputs, output can be 0, 1, or 2 For a full-adder, 3 inputs, output can be 0, 1, 2, or 3 c[i] b[i] a[i] count c[i+1] s[i] 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 2 1 0 1 0 0 1 0 1 1 0 1 2 1 0 1 1 0 2 1 0 1 1 1 3 1 1
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8 (c) 2005 - 2012 W. J. Dally
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