1Digital DesignCopyright © 2006Frank VahidDigital DesignChapter 2: Combinational Logic DesignSlides to accompany the textbook Digital Design, First Edition, by Frank Vahid, John Wiley and Sons Publishers, 2007. http://www.ddvahid.comCopyright © 2007 Frank VahidInstructors of courses requiring Vahid's Digital Design textbook (published by John Wiley and Sons) have permission to modify and use these slides for customary course-related activities, subject to keeping this copyright notice in place and unmodified. These slides may be posted as unanimatedpdf versions on publicly-accessible course websites.. PowerPoint source (or pdf with animations) may notbe posted to publicly-accessible websites, but may be posted for students on internal protected sites or distributed directly to students by other electronic means. Instructors may make printouts of the slides available to students for a reasonable photocopying charge, without incurring royalties. Any other use requires explicit permission. Instructors may obtain PowerPoint source or obtain special use permissions from Wiley – see http://www.ddvahid.comfor information.2Digital DesignCopyright © 2006Frank VahidExample: Seat Belt Warning Light System• Design circuit for warning light•Sensors– s=1: seat belt fastened– k=1: key inserted– p=1: person in seat• Capture Boolean equation– person in seat, and seat belt not fastened, and key inserted• Convert equation to circuit•Notice – Boolean algebra enables easy capture as equation and conversion to circuit• How design with switches?• Of course, logic gates are built from switches, but we think at level of logic gates, not switchesw = p AND NOT(s) AND kkpswBeltWarn3Digital DesignCopyright © 2006Frank VahidBCD to 7-Segment Displayabcdefg = 1111110 0110000 1101101afbdgec(b)(a)4Digital DesignCopyright © 2006Frank VahidDecoders and Muxes• Decoder: Popular combinational logic building block, in addition to logic gates– Converts input binary number to one high output• 2-input decoder: four possible input binary numbers– So has four outputs, one for each possible input binary number• Internal design– AND gate for each output to detect input combination• Decoder with enable e– Outputs all 0 if e=0– Regular behavior if e=1• n-input decoder: 2noutputs2.9i0i1d0d1d2d3 111000i0i1d0d1d2d3 000001i0i1d0d1d2d3i0i1d0d1d2d3001010010100i0d0d1d2d3i1i0i1d0d1d2d3e1111000ei0i1d0d1d2d3 0110000i1’i0’i1’i0i1i0’i1i05Digital DesignCopyright © 2006Frank VahidDecoder Example• New Year’s Eve Countdown Display– Microprocessor counts from 59 down to 0 in binary on 6-bit output– Want illuminate one of 60 lights for each binary number– Use 6x64 decoder• 4 outputs unusedd0d1d2d3i0i1i2i3i4i5e6x64dcdd58d59d60d61d62d63Microprocessor0HappyNew Year1235859a0100000010002211000000100001000000100000006Digital DesignCopyright © 2006Frank VahidMultiplexor (Mux)• Mux: Another popular combinational building block– Routes one of its N data inputs to its one output, based on binary value of select inputs• 4 input mux Æ needs 2 select inputs to indicate which input to route through• 8 input mux Æ 3 select inputs • N inputs Æ log2(N) selects– Like a railyard switch7Digital DesignCopyright © 2006Frank VahidMux Internal Designs0di0i12×1i1i0s01d2×1i1i0s00d2×1i1i0s0d0i0 (1*i0=i0)i0(0+i0=i0)102x1 muxi04×1i2i1i3s1 s0ds0di0i1i2i3s14x1 mux0a8Digital DesignCopyright © 2006Frank VahidMux Example• City mayor can set four switches up or down, representing his/her vote on each of four proposals, numbered 0, 1, 2, 3• City manager can display any such vote on large green/red LED (light) by setting two switches to represent binary 0, 1, 2, or 3• Use 4x1 muxi04x1i2i1i3s1 s0d1234Mayor’s switchesPrmanager'sswitchesGreen/RedLEDon/off9Digital DesignCopyright © 2006Frank VahidMuxes Commonly Together -- N-bit Mux• Ex: Two 4-bit inputs, A (a3 a2 a1 a0), and B (b3 b2 b1 b0)– 4-bit 2x1 mux (just four 2x1 muxes sharing a select line) can select between A or Bi0s0i12×1di0s0i12×1di0s0i12×1di0s0i12×1da3b3I0s0s0I14-bit2x1DCABa2b2a1b1a0b0s04C444c3c2c1c0is shortforSimplifyingnotation:10Digital DesignCopyright © 2006Frank VahidN-bit Mux Example• Four possible display items– Temperature (T), Average miles-per-gallon (A), Instantaneous mpg (I), and Miles remaining (M) -- each is 8-bits wide– Choose which to display using two inputs x and y– Use 8-bit 4x1 mux11Digital DesignCopyright © 2006Frank VahidAdditional ConsiderationsNon-Ideal Gate Behavior -- Delay• Real gates have some delay– Outputs don’t change immediately after inputs