EE101Lecture14

EE101Lecture14 - Introduction to Digital Logic Lecture 14:...

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© Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 14: Adders Radix Complement Multipliers
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© Mark Redekopp, All rights reserved Radix Complement If we need to subtract 2 hours on a clock there are 2 ways to do it. Subtract 2 or add 10 12 1 2 3 4 5 6 11 10 9 8 7 12 1 2 3 4 5 6 11 10 9 8 7
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© Mark Redekopp, All rights reserved Radix Complement The same technique can be done if we limit ourselves to a fixed amount of digits Using 2 digits, to perform 4 2 we can subtract 2 or add 98 00 01 02 03 04 . . 99 98 . . . 00 01 02 03 04 . . 99 98 . . . -2 +98
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© Mark Redekopp, All rights reserved Radix Complement 12 1 2 3 9 10 11 4 8 7 5 6 12 1 2 3 9 10 11 4 8 7 5 6 00 01 02 03 98 99 04 . . . . 00 01 02 03 98 99 04 . . . . 0000 0001 0010 0011 1110 1111 0100 . . . . 0000 0001 0010 0011 1110 1111 0100 . . . . 10’s complement 2’s complement Clock Analogy Subtract 2 Add 10 Subtract 2 Add 98 Subtract 2 Add 14
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© Mark Redekopp, All rights reserved Radix Complement The radix complement of a number, ( X) r , with n digits can be found using the following formula r’s complement of X r = r n - X or (r n -1) X + 1 This is the r- 1’s complement base r
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© Mark Redekopp, All rights reserved Radix Complement r’s complement of X r = r n - X or (r n -1) X + 1 10’s comp. of 3841 10 7’s comp. of 2350 7 16’s comp. of EC47 16 3841 10 9999 10 (r n -1) - X 6158 10 + 1 10 + 1 10 6159 10 9’s comp 10’s comp 2350 7 6666 7 (r n -1) - X 4316 7 + 1 7 + 1 7 4320 7 6’s comp 7’s comp EC47 16 FFFF 16 (r n -1) - X 13B8 16 + 1 16 + 1 16 13B9 16 15’s comp 16’s comp Important: (r n -1) is always the largest number possible for n-digits of base r and is thus n copies of the digit (r-1)
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© Mark Redekopp, All rights reserved Hex Values • Any string of 1’s and 0’s can be converted to hex To understand the meaning of a hex number we must know the underlying binary system A 3 1010 0011 +163 (Unsigned) -93 (2’s comp.) When you see hex, you must know what binary system the underlying 1’s and 0’s are using hex bin
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© Mark Redekopp, All rights reserved Hex Values Unsigned • Signed (2’s comp.) A 3 16 16 0 16 1 = 10*16 + 3 = 163 A 3 16 FF - A3 5C + 1 5D 1 010 MSB = 1
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EE101Lecture14 - Introduction to Digital Logic Lecture 14:...

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