ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS

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1 C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h prolm is, how you'r solvin th prolm n wht your nswr is You lso n to inlu rwins o ll iruits s wll s pproprit rphs n tls In th lst Invstition w look t som o th si proprtis o th inputs n outputs o loi iruits Th ojtiv o this n th nt svrl Invstitions is to look t som si MSI (Mium Sl Intrtion) loi iruits m rom 2 to ts tht r vry usul in mny pplitions In this invstition w look t nors n ors or trnsltin t rom on o to nothr lik rom sin mnitu to 2's omplmnt W in with rviw prolm Givn th ollowin loi iruit with truth tl s ollows Fin th truth tl whn th nl n outputs r tiv low s ollows 2 Dors n nors r vry importnt loi iruits tht onvrt t rom on o to nothr Binry ors in prtiulr r loi iruits lik th ollowin 2-to-4 or with n=2 inputs n N = 2 n = 2 2 = 4 outputs n th ollowin Truth Tl

2 Dsri wht this or is oin Mmoriz this rltionship 3 On possil pplition o 2-to-4 or lik th on in Prolm (2) is tri liht ontrollr with ontrollin th lihts on Min Strt s ollows - Grn Liht n WALK sinl - DON'T WALK sinl - Yllow Liht - Liht s th input X X os rom to Com up with your own pplition o or tht is irnt rom thos o your rins 4 Drw rliztion o th 2-to-4 or in Prolm (2) rom AND ts n INVTS You n us ts with mor thn two inputs 5 Suppos th 2-to-4 or in Prolm (2) is hn so tht now th nl n th outputs r tiv low Drw th hip irm Drw th loi irm to rliz th iruit Writ out th truth tl 6 On o th rlly usul turs o MSI iruits lik ors is tht thy n put tothr to orm lrr ors Givn th ollowin 3-to-8 or m rom two 2-to-4 ors Y4 Y5 Y6 Y7 Writ th truth tl Dsri wht's oin on in this loi iruit 7 Th ojtiv o this prolm is to introu svn-smnt isplys I w look losly t iitl wths n loks w s svn-smnt isplys s ollows 2

3 with smnts (lins) tht liht up to orm th irnt numrs Whih o th smnts liht up to orm th numrs Up to now w'v only n workin with inry ors tht hv on output ssrt t tim But mor nrl ors lik th ollowin BCD to svn-smnt or BL typilly hv mny outputs ssrt t tim Vriy this t y writin out th truth tl or th svn-smnt or ov tht tlls th isply whih smnts to turn ON n whih to kp OFF or h BCD numr rom to 9 Not tht whn th input BL= th isply is lnk - ll smnts r OFF An whn BL= th BCD input is o Also not tht thr r mny othr usul ors lik BCD-to-Binry n Binry-to-BCD 9 As w'v sn ov th output o inry or lik th ollowin tlls us th vlu o th inry numr t th input Th orrsponin inry nor s ollows os just th opposit It tlls us th inry o o th slt input 3

4 Writ th Truth Tl o th inry nor i only on input n slt t tim liz your nor with O ts plin th oprtion o th th ollowin iruit 5 volts 2 3 Kyor-to-BCD X9 onsistin o lultor kyor onnt to kyor-to-bcd nor In th prvious two prolms w'v n ssumin tht only on input woul slt t tim But thr r mny situtions in rl pplitions whr mor thn on input is "omptin or ttntion" lik whn svrl usrs r tryin to ss shr printr t th sm tim On wy to hnl this sitution is with priority nors Whn mor thn on input is slt th priority nor nos th on with th hihst priority Lt's suppos th ollowin is priority nor with hvin th hihst priority n th lowst Th trik in sinin suh iruit is to irst sin "prioritizr" n thn onnt it to "rulr" nor s ollows PIOITIZ H H H2 H3 D D D2 D3 4

5 with truth tl s ollows H H H2 H3 M M How n you tll rom th truth tl tht hs th hihst priority How n you tll rom th truth tl tht hs th lowst priority Dsin th prioritizr Dsri in wors th ovrll oprtion o th iruit 2 Th ojtiv o this prolm is to show how ors n us to rliz nrl loi qutions Suppos or mpl tht w wnt to rliz th ollowin loi qution F = X' Y' + X Y' Writ th Truth Tl or F Mk us o your truth tl in prt () to plin why F n rliz with 2-to-4 or s ollows X Y F Us 2-to-4 or with tiv hih inputs n outputs to rliz F = X Y' + X' Y pt prt () i th input o th or is tiv hih n th output tiv low Mmoriz th rsults o this prolm 5