M16_2_EEM16_W10_L15

# M16_2_EEM16_W10_L15 - 2 Perform the mod operation ± Does...

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EEM16/CSM51A: Logic Design of Digital Systems Lecture #15 Ch 10: Arithmetic combinational modules and networks Prof. Danijela Cabric Fall 2011

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Arithmetic with Signed Numbers ± Two common representations: ± Sign and magnitude (SM) ± True and complement (TC) 2
Sign and Magnitude Systems 3 0000 0111 0011 1011 1111 1110 1101 1100 1010 1001 1000 0110 0101 0100 0010 0001 +0 +1 +2 +3 +4 +5 +6 +7 -0 -1 -2 -3 -4 -5 -6 -7 0 100 = + 4 1 100 = - 4 + -

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Representing Signed Integers by Two’s Complement 4
Two’s Complement System 5

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Two’s complement for n=4 6 0000 0111 0011 1011 1111 1110 1101 1100 1010 1001 1000 0110 0101 0100 0010 0001 +0 +1 +2 +3 +4 +5 +6 +7 -8 -7 -6 -5 -4 -3 -2 -1 0 100 = + 4 1 100 = - 4 + -
Mapping in Two’s complement system 7

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Converse Mapping 8
Example of Converse Mapping 9

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One’s complement System 10 0000 0111 0011 1011 1111 1110 1101 1100 1010 1001 1000 0110 0101 0100 0010 0001 +0 +1 +2 +3 +4 +5 +6 +7 -7 -6 -5 -4 -3 -2 -1 -0 0 100 = + 4 1 011 = - 4 + -
Mapping in One’s complement System 11

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Addition in Two’s Complement System 12
Addition in Two’s Complement: Summary 1. Add x R and y R (use adder for positive operands)

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Unformatted text preview: 2. Perform the mod operation ± Does not depend on the relative magnitudes of the operands and on their signs (simpler that in sign ‐ and ‐ magnitude system) 13 The mod opertion 14 Two’s complement Adder Module 15 Examples 16 Change of Sign in 2’s Complement System 17 Simpler way 18 Change of Sign Procedure 19 Subtraction in Two’s Complement System 20 Summary of Two’s Complement Operations 21 Overflow Detection in Addition 22 Two’s Complement Arithmetic Unit 23 Implementation of Arithmetic Unit 24 Control Signals for Arithmetic Unit 25 Arithmetic Logic Unit (ALU) 26 Network of ALU modules 27 Comparator Module 28 Binary Description 29 4 ‐ bit Comparator Module 30 Iterative Comparator Network 31 Tree comparator 32 Multipliers 33 Multiplication Bit Matrix 34 Implementation of 8x6 multiplier 35 Multiplier Delay 36...
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