Issues in HW

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Issues in HW1
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1Complement Subtraction

• To calculate M-N do the following
• Let Q 1s complement of N
• Let S M Q
• If there is and end carry in step 2, then Answer
  Add 1 to the LSB of S
• If there is no end-carry in step 2, then Answer
  -1 x (1s complement of S)

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1Complement Subtraction

• Example Calculate 1210 1410.
• Lets use 5 bit representation
• M 12 01100 and N 14 01110
• Q 10001
• S M Q 11101
• Since there was no end-carry
• Answer - 00010 (-2)10

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1Complement Subtraction

• Example Calculate 810 310.
• Lets use 6 bit representation
• M 8 001000 and N 3 000011
• Q 111100
• S M Q 000100 with an end carry as 1
• Since there was an end-carry
• Answer 00100 00001 00101 (5)10

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2s Complement Numbers

• 3-bit example

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2s Complement Subtraction

• Example Calculate 1210 1410.
• Assume 8 bit representation.
• M 12 00001100, N1400001110
• 1210 1410 (12)10 (-14)10
• P -14 11110010
• S MP 11111110
• 11111110 (-2)10 in 2s complement

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2s Complement Subtraction

• Example Calculate 1610 1410.
• Assume 8 bit representation.
• M 16 00010000, N00001110
• 1610 1410 (16)10 (-14)10
• P -14 11110010
• S MP 00000010 with end-carry1
• Disregard the end carry
• 00000010 (2)10 in 2s complement

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2s Complement Subtraction

• Example Calculate S -1610 1410.
• Assume 8 bit representation.
• M 16 00010000, N1400001110
• -1610 1410 (-16)10 (-14)10
• O -16 11110000, P -14 11110010
• S OP 11100010 with end-carry1
• Disregard the end carry
• 11100010 - 3010 in 2s complement

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2s Complement of fraction

• Find 2s complement of 100.00101
• N 100.00101
• n3
• Let P denote 2s complement of N
• P 23 100.00101 1000 100.00101
• Thus P 011.11011

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1s Complement of fraction

• Find 1s complement of 100.00101
• N 100.00101
• n3, m5
• Let Q denote 1s complement
• Q 23 2-5 - 100.00101
• Or Q 1000 0.00001 - 100.00101
• Thus Q 011.11010

n
m
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10s complement

• 10s complement of an n digit number N is
  defined as
• 10n N
• 8 ? 10 8 2 for one digit representation
• 21 ? 100 21 79 for 2 digit representation
• 098 ? 1000 098 002 for 2 digit
• 008 ? 1000 008 992 for 3 digit

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10s complement

• Calculate 86 9 using 10s complement
• Lets use 2 digit representation
• 86 9 86 09
• 09 ? 100 09 91 in 10s complement
• 86 91 77 with end-carry 1
• Disregard the end-carry
• Answer 77

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10s complement

• Calculate 9 86 using 10s complement
• Lets use 3 digit representation
• 9 86 009 086
• 086 ? 1000 086 914 in 10s complement
• 009 914 923 with no end-carry
• Take 10s complement and multiply by -1
• 923 ? 1000 923 077
• Answer -077 or -77