ENGIN112-F07-02-Number Systems

ENGIN112-F07-02-Number Systems - complement representation?...

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1 Tilman Wolf Department of Electrical and Computer Engineering 9/13/07 ENGIN 112 – Discussions 2 Number Systems Engin112 – 9/13/07 2 Binary Numbers
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2 Engin112 – 9/13/07 3 Base Conversion ± What is the decimal equivalent of the following numbers? y (53) 7 y (1010) 3 y (1010) 2 y (1010) 10 y (A0) 11 Engin112 – 9/13/07 4 Base Conversion ± Convert (38) 10 into base 2:
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3 Engin112 – 9/13/07 5 Base Conversion ± Convert (38) 10 into base 16: ± Convert the result into base 2: Engin112 – 9/13/07 6 Counting in Binary ± How far can you count with n bits?
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4 Engin112 – 9/13/07 7 Binary Addition ± (11011) 2 + (01101) 2 Engin112 – 9/13/07 8 Binary Multiplication ± (11011) 2 × (101) 2
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5 Engin112 – 9/13/07 9 Negative Numbers ± How are negative numbers represented? Engin112 – 9/13/07 10 2’s Complement ± 4-bit numbers: ± Conversion between binary number and its 2’s
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Unformatted text preview: complement representation? 1000 0001 0000 0100 0111 0010 0011 0101 0110 1001 1010 1011 1100 1101 1110 1111 +1 +2 +3 +4 +5 +6-8 +7-2-1-3-4-5-6-7 6 Engin112 9/13/07 11 2s Complement Arithmetic Subtraction using 2s complement: (11011) 2 (01101) 2 Engin112 9/13/07 12 Odometer Example What base? 7 Engin112 9/13/07 13 Odometer Example Going reverse Engin112 9/13/07 14 Odometer Arithmetic Experiment*: 1. Reset trip odometer 2. Drive (forward in straight line) 3. Trip odometer reads: 4. Reset trip odometer 5. Drive (backward in straight line) 6. Trip odometer reads: What far are you from the starting point? *Professional driver on closed course. Do not try this at home....
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ENGIN112-F07-02-Number Systems - complement representation?...

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