From 5437778e30cdb37acb6c8d8e5fb3f02deb09a03c Mon Sep 17 00:00:00 2001 From: shockrahwow Date: Tue, 2 Oct 2018 22:48:10 -0700 Subject: [PATCH] adding lec10 half adder --- cst337/img/fig0lec10.png | Bin 0 -> 11377 bytes cst337/lec/lec10.md | 30 +++++++++++++++++++++++++++++- 2 files changed, 29 insertions(+), 1 deletion(-) create mode 100644 cst337/img/fig0lec10.png diff --git a/cst337/img/fig0lec10.png b/cst337/img/fig0lec10.png new file mode 100644 index 0000000000000000000000000000000000000000..e064e1144bd0417f2ceed80dff17be6b0a0d01f7 GIT binary patch literal 11377 zcmdsdg8O-1g{u6TNH45J*@lZ4M1_171Zx3KH|2-!BMFt-g6Q39Ec0T^Eylesf z{{BLaZqD8|uRLsp+`a5GcV+OL9s*#>iUt8$zZd+|1Z>l54lW?e%%73}Qc(>jL-P1x z!j#yZH;>-ur2%N(JF4i>`FK76bH|YKDOxC~*lHou6!hLaWKdQ#y7!QIMbcv>1R-Pi z(s;_}#K+j!U(0`?16NkwV!s`Fk)DyhTfB5*%>?iXjz^fB6;%f_3i8S^KXbcCSI}2#^d@V>JEJQ!*T7wIl+_svV~)da_4wt=KQq zChILDT5t-9>U4CQ33SXnnq;@i8a>(tZIE#)lx_^NUvFv)nOxtSt=^Seh`Rv~62|d# zvF?H@EcZ84AbD45*-JE!MFA%uCaMMN$}DiJ#L?;7MpzltK?hI;m;_iU)_47dYb=Yx zKX?8l+eG-?JNW1*S>tp#|LeDfwcLT((e(UpKG*FFevelhjc&+Vjk55|!M&I1E0+&ir5Z>P%_H+Ee$rw-QL8O)^$Rtwj>e-|vD3xx=ak%ni9= z*_Xs^2;`|Uk7JG9a2jg=)0=ffM$*lzC{OZEO>3rQ;T5H+rL-){1x=Ur zqnNc2M_s>9CMUb<*6br0!5sS>m*&5_#2nk>n34=V{WedMvF$H6wLE1$kZwG%CFCsq z)J;uupBp(vC(t3xdoxSDTK0WIIr`5p<*CrWPaJ_G8EqPKqxzmIG#Ia>N=L z1UQ@E6&7xvN)=O3#jJd}w4hN-_ht&RPDedA9}{7!+&9GIaIKr#{*4*zqHpNIC~eEF zK!aV&myJB9iAiyz$x}jBb9H}wVR$atd$ukJWHsFCMjI&4J`kTsYx4_BNxIQ@q|$mk z2kfRA+a8-LwN;+_8C^T4c-6zButbnE_T#_{?lSk-ku_KvIIpG2IQ)8nTVbgu>qtJE zFH7ZUaF2re3b(*Yw+@mj*wW!HwKoT8L@^l6J$Te%Sad0|hkKeBuqv6jk-Xy$ihF4H z3D(xjqrfJl+kJ$L^g0eHv57k8lLZF3RegUEOtxj%bl9;~+gflPl5>51(mri}rdKDo zFO)&7`xp@Soz~^JD2Ct;clEcENd0^!`9dBAo=v`xSMk7sPm;lwiexoOP-YzUi&-9I z=-reKY2F(&^=ihh9hex9Iyw)!_S|`+>))%6oP5}9Hx|Sy#MON8!U+UTHPM!rJ;=Rp zK5`agp}Qxf8`(AY7ej)DXByMk2rnY}QK{>$*qg=J`j-kdiC=lv-Scuf674CYTZ&di zXsKIo>C?<`R&z)EHW=UVy>~esZ)TVVyxpPVR8n5 zCg!^SG)yMF z%a4-=>&F~95_Y3JVV+JhoGW%Lz}dCw_n9%FU`ZJ_HOYlJK^Fg|>@31eMWqb;C1!^y zL6ovXP!6VTNolVqVp+s&g}BUq97=I1MB4Q(CQ91Bs#?5}Up>yUupQbG9d4aKUU>Ps z>eUFvrpAw6v+>Hhy$UIMW&CRbd)%4>uge^rSg7VV3Cr5is*uUPjk7QANGnBOOIXD$PQkGdzm^TX6Jw6cyMEBF9oxh#ji@iDLe_^IKWH$i(&J71B23WW z>j(^6)Wpi;f?5x!zY=*`p@tBJJq@^pnzvgW1pU(?;zDe9{TUw3$Qgq8TVMdoQin~OqiO!S}5AAP7; z#UpKw>kdDNm9EfM?R6rG?jRc#p47odzbRq*T%agGymoml2Ya`!nqcwY@r4Ka(sR_7 zu$h@uHXiQi`a?Hs9NzFhZ2o%4%AWG|l;uD^E3R1b-l^N+)p!y1CU~2ses?j5{uEN{ zdH$+rssYlFf99MSP+T~p%$*kYCjDVX`$cVxLx#EF(U%tUtgo{7f()JG%cYQ1wd^%g zl{9&(s9mg0l#X*7w?cFj-C#WTI>Jz*_rRO8hE7CmgMfpo8SUUJUHQEc8rq63rMsW4 zQC}rPm6m&U&Z+$Ds8oD?1K{2xb4_@FSnRP?9{qE?b`X*ud=b+xd3LhOrm43%K? zJTO4M_Sx^%sDp4PiD)%}4s9}K*<^ZXsKm&6-uW!IWRS1y$lX7w_cmn`H>#@Qsbc9~ zoN@0{p}%!tZ+yjpy+a=J|MbW{HML*8_zEp-+X^Go{d$Gn)|TS^x%FmU=TnDbwy&pf ztS9YP-4O1|=P%MTKjvupJpOX@v%l#?_!xRtu>&a#@jAjU*ZSxq+`=vWmR{l9HJ|V(RXMejuAEFgx#@mm zYo9lp4n+6YX;x?yL6EVT4o7d*rnj?xyLq(e$&roN%`?pmwQiv6T?>^8b{}yMxdac` z_DC~Uq17)ph?WK%WLU+Z+;K^;zXMvgr+)mIrtwhP9?7;{e5* z+oyV&-Uy|OsS&F~vF!VU4u)!bC)L&rMmviX5{6GlWI2%s?UBl0rm&+(au^4ZV3z%dg?;m)F>ghtX2G zi=Qv`F#JgW;h@R%jBJ&i;=fAy{HywKJ@v1|`qF(-wh!9TGC3+PJ%=sxff`~bH_!IO zWa{iTx516%0g@wx4UZ4}TbL5N83(xR(7(YUtO0a>2^yA7s8joyFWU-E9KXW^nm-@? zfSpPGrhfTOb!_Xi2|;V#tOxX=Z6!gQO;rxU*>mtLeJ}ULeqhiSp@WVaM~-y&38_DE zwCnHd0lzyxm?16x(JhN)n|(ASr4pE>`+lXb*)zgL}e)TcrCq;bNJA2Bq) zTCa3Kpx*`UomN%>>Jlxi@Pq=_sDI(78A$d~Jzdo$8fh+)SrZyBP} z;gP-qADesq*(>K(vUawI=O`;<7G~e46`n%j*|`;#sMlALm={GQn|>K|M*q-D*T0Gs zU8rIhce{umO$We^_j#;=2ONg4F=y+_&RurcjfU+3g4+1$i>RrEYHEHL4bwAE@guV= zZ(yvlBaw$gs;@i9Leb}yW$&6TEDk)V5jWOSag;y5YABsGSCz@<>t0d}ITO`Mjiii_iu ztK*wr^oK9s*#&fZ z^4>=8rk9c6s>DL}w>ZyI^2Wlnd-0XepC)Wq(M(Xs{7S3w#$Z!YSJ6hG7|QgchUn&3 z#oKZf5GO45Az{k(TiZ>qzBu9tS0pv?TSkgZDd%^J9F#Ry9Ho=bSNvr3r zQI!OX2A%@jI;JGUni({i<_uxTj-jwo;1y(3Vs$>O2~+ z%`2oDkxs$!DWBsbO=OuTjpss(=DYT z!~g@#!w*%dwf=osaQxk#Z^H)bG#5`9+;CMp>oNXm0(q9+eZs9u(d#C}2Ps8fKw?8gV{}f&Kb*ldvkQ5AevkFDrIUsObsG07Vb_Z<^f6m zmq4wIjV5oz16q4@vKp1_%=O=;+otEwSJxr$l6bd^9Ch)R%FNX7G1 zT`d($)y57a9wPV!IeZTpSAygTT=YBz&;@eo07HAhmD!VKQ5PpmMkX#N3GGj{fI`6& zH1s=O*~ButxZkN%WF#R9>QT_-FDO?qH)^4d3&z0qrMGS zgRJoTXjIKxOsO>I-1S>6VF@FGSnh5J+JU_J?G|m~cqXY9-sG7j%+s=Tj=2XuNZnl* z2Txb@DilyPVDUmJuE#m)b=MIYTm9$<%O%d=(C^3IwMlqBao1W=9GF2`F{wlt9hDA2 zKi8S{{nEH<8o^%;k0TT(6yj>=H5oZ@fmuqXY-#MS2T(TBo-)>S?<-B-@n#J9LQ6B% zkxC(J`U`q4iQg8bE~*0ZHO!||?`;yg)Ds9EAuLd#quX&Ly1sTG{;0_a2EyKxmJj(s zPZOuqog%QFE)Yz1ft1wbz6Df8) zXe{kKF(%9**ddpRe=hokbwAWP`0}4eTB^?6UnvX?tlDOx)Pjsak;}fR>ZyAmTw#2m z@$#<4*;F!fZdbIW^~6ki2k!j)fm<+U8~UmwwKz!hcV)1v?!H7>;UAvYJ$MMIgFlyKify}wQZyL~e7IApZ zbO7O3%(sDcB)^^3Ln>BTO+Ttv6KTYAUiJbZRO<#?pMf?BW?=r9Tm2p&8YIY3h`Erw zeNfPrJuN*Z(revc;E7Z$lYO|M%@eplj~65E>^^Tt%(R^9`nl)Jrxwp+H8+HjUf|p8 z@Ru}#oAO{Qt^WLEgM_dt;G5}d_^YD079@i$VM#5Vba=n8$D|?JpjMRnA#!hRd!{~S8S1BreCI5-67;y>Xu88sT&H&_V&REO+dn3&_8^I5 zcn2|zi#PbOu)`wd1M4fGOk}}gt8kNSDm`|-oQ~_OeD`h!$D&$Hq6PUWb8TO6!cs&5 znv4Tz_T(gB1dyYo@1B#3Hvt`E?q|&zgduOHhka;0nD>S9AE=E&^^EAIt3`b)Fi*nA zGc2t;>sV|4neK4z(8I16b01c}`5*wT(EfNXIB7?Lp%Z4YZ63OQ8?>T?u6^E38DiWFi6F2~E6^hC zFjjWj#0oG?-nW_T#s>cvE{uP3peeR#=2j-0jfYjP2Zq?}_0d>~#D$`IiRvSf<1JtQxY8urN~|>tlwe{$(3(eY}*7@f>$P z(1VpFk$fQ0HTC0e_DBJm(>>}S73p*2t;H-grV+OioH7nXWTevEATD0yR>{FK#5Iwc z$X?<2F3kEW9_3@_y*a=`sl6K*a}*cPD7pIBsyaMt>=S>qHu^Q_9}-=Lb_I)WXH=|D zuS!*T22_fNZ6)3lt-p7oHU#>T#*00-YC>?(rq98&i(PSM?MbsMLAmaaSpgO zdFx!NM&az0S*n^}13M9)JNXWvB3XJb7vqj(qgqYhWq`+^pQA`VKr<$Z+7(?KLda?x z?W)&x)O*>qd??80_^?JS1zjvzN3Z4?Hg zpO1NB8^{m`Ql-mFBEJGDC;%VzoIyJm2)QT}j3TcSs$a`=33 zq@LE}v4?O1_K#EBnxFWOhW;(pj7tIbznEZ&rnW>i2REI#Ki2~oL2M%{jPLF3Ag#1~ z*dMTbJtD9UgD$4Ti{&ScKd~{Kttg zXbM0F>2^n65V0f`{2Iaw+I0xBxQw$Ss^Jr+Godk&l@tf&Br%%YRM0O0^a~#0G2qrh_oQx z*_Z@n=g~$Jic{#w`qPmgo`m~{>Kw@i{M-uM3Rl9w?WIr1uYlBHH4rVR8?wY?djUEb zwp>Y+*CsS#3i}tm{r%P|u;C-4AR>=@v5;jec>iz(Uj*NlFV>{kNKl4{nq)CDd05yE#R+#TKszRm%59PW6K!wNBN{km zfOI@iu6wQES4sHuGQGb>j0hfWi0;t;B{O+U=*CrbaCezh^TzFCH<)5H3)@;Ac}P5( zMIflXopjj60rcW>fMx8sz!|Spk+zt*s2Tk^1BUVY?F1DGfg#ZS8P?uhZJ+4E4UjuO zyAaF?PWnMm;i`tvA)tZBC?)4%3QK_Dm!I{21TxISgo>t#=Y5fpqQ~=Z`wAUC*E#?X zDa_GQE!5M%Q@#-`AF0~7;b2s9QE`Nlcl?rK?es1fA8LvRwgUH|&E}k2B0Wu+G=h4L zPiF@(>wj*ZOOj4AO=q0Ww5$8iWyz$U=6w;`w^`nnTcv;Z1y$fjW9`bpYYDKpGq3l` zLZ8cYQaNjRv?3THi#4qr?)S82}HLnlwX;F8Ec5+U!8a<%%oou3>D z$QnU5cNTvfEu{qR9w%1IK4|1Kw)f*t8?x(dl{}l3S-#I95M2s>zJZH&xL&a9+nHMT zF75i?6*0)RA2YGor^6N>^R=aIJncClJ7|(u^L`^TQHw53jNMV#RR!Oux7Kdpdbt%| z_Jv$!V^0fT)<5!AF6ws|eYxlNVCRbi1Vi&jyvvEtovSO;H(0Ra+2$JV-~OhjJ`A0! zUPHA?8^OUo3{yZ$Ipg&mP-4MifgpoCSHrYK{8mO_UVebzplrK`+E5FHhs&-rDQYbQ zcyKM6Yhv~=Tk&axN%r}(P*9)vR7Xk+@zt%M2!IY@Nd*Z-rIhFJ)haB<% z^?1)OM@DeU;K?iO(ku(scRJSLBdm=f4a}^sPxd14L)slcLWmoB{w2|+r1#=?_8*_9 z?EY7GN`f-Mh>s)G^-e0DmoZ(%d$!8BZefe;z{Nt$t9sUet4GUX(67{&{*gg-f(pMf zH2INrNMn%B>%$bTmwm}F^TI0bE+yIIfU&`@uT%pIehUH&AKKk?C@sBgr!zK;3fHmE zlFw}E?5J&q4=Z0ic75SKBdB0{?@fyOzSs(zRU53u(x@8xKInpfg!+$k{+FK!)PWfP zJLc}o{wsuVmX_t$yg(Sz#<7EA|5?7dn=~WaY0l`zeCsB)Ap2v&uo)!=)PS43!o{~` zQsfe~Wd>zOi?*fNQIuPrfoY{Y+egWnKpGGI=p!TQ)j>C+uw>pN&-`SU{DOdj@bX~N zVg9Ykj=4|A3F1G?rRJ#3?KJ^B2K$$Y;)4^9A0KkO*)neKJ>AXkCl=dWn*Z5)36CT8 z)$?y4ba<2Ydm`3Fqw8))OWNULvSf5{Qwjh;x^nw2fWPEGl)c`OKQ2>F3BnK);iz&X9X>{J2VX1WboL`YYj0fFbg^4LiwS-c zKy%q4)O+8N;X-;p8?+vWJ8a#fDi0arXil?Ak#Xb7L}gRVTRp65ZHw}hDP3(5@CPL< z7gXmyhFo8dgO@@K3W>|_S^q=clBtqysTmV4Nq)+)uiDGRDVkiEe$mMo=_B371rXbE zyBo52_NP5(grk}5P8g5Kump?nf)H>PZL<2v*C}4)%h8|yE8?y8%)NW?jaj#z)ok_m z#YT9?TFSh{y|_lfZbqBa<$=Bo4nIa;;C!S!|J|UTi;{UDk!CVoZ9GNy$eXi`OUr&# z4Vj}Tu$A`GWgmm*7gec$Xr)bdy1PcZJm0^{W4rqj=I(hD^&C`hNU@%Tk2eYqTO-m^ z+670@`{(R3_I|Sm@06YUYKXCN>05&{)TeatqRB3pz*S?lLb_GU+YTKc-U06BZ-2q< zS!dT|88mr&)TBBaELs+k+Ji-sz+UaWJzoK>20}NMva_~$=u@TSfPAU6WuQT5Fh7vf!WX~fFuti{3<8w<&Lh`7m95pzr%!5x-ge{Uj>A(fF_09$a5ZS@4j05G|FJUofXTr5@KT5dd0Ve>u*Q~`0*1=<0 z4oOcg_>ZUhuYLy$WLjz-rd%rli7x!5ZX>l(>q}~hh^^UE3^JEr-r=P0K5j5gsX{r+ z*J$^E7W&nQS*u?;v-ch03PX{Y*vZL5yGdJO`InkEmeGN9_Pfqqf~ z_@I+93m4@$R!(gbPGl>x|2$*q&vo=x%JyI1>oY9ocg3ePnJ-fE=D$2G$3yR5`Sy`_ zKFgqqvT^LMFjL<-HfqT99y()O4t$X`^X9az=vpzRt+#KG+B|b3wBPIuu;A*5ep;@; zFk!K90(ya%ClB*+(WwW?D(`_UgMFD3Pogh452VI+W1T`d4oq|S{k1cXralJVlr0Gd zZXS+jV0TJFG@~8lm&IG?roXuk_Vn!%{v8wQt3Pa}t<|O^HNV&E27P%E>98BrHyfcA z@VS;{a%0|pW3VM^l4Ou<`3^kqf?yyR>Q_fMEy_shsctC()R)&pKJSyn?%_g}0;+UI z&$TXv@-sIzl=FQ!Y7?(UX*aE4M~qJbmj<&DO#6CpyXokt$&y5rsrE0)smfJ>rqZ!1ZwzLkWujF`DJ?*>*!Hi_7<&k@*OST zEUlxvKPp`aE-U-aji~!T{hZW=mnTaf%3FE~?lAT^1zpmZ6b?xhi-J#~ZC5$%Iu|Kl z$E$p9{5|d+c>5&+T$L**CdzWaL8ncIFSr%9BT0rG(zSLTKT$mTv#vNxaLQNPWB1e@ ziFhau{_Xd7IwW6(cZn}SHcaElrSNy!JYT|+P{B6A){~}F{7WODZ2_#YH^2S5E3v-6 z{9LBuFb`O^TXN}zbFUX$U`T+~GaMw~HFcg@<+;Q_mMTO(m_`g(U}XVoO?RQVY+5lH z&mN))e#=79YL6Ofks1-KB^Bx9XNjz*Y-DQ8nwD+by1&N*8sZ|_tkU+WyCgp)shlcK zSAv8yQR0>hNc8v?rtZQkhV_fY$2=Yq`@4qc`{(9%9M-Oct@i^6PVMlw)&FxDEGn&& zIRpZD_!>s?pD7*)2crygiZ77w=1^GSfx@;}Q^Yy)5l=W!}iLA8aWA){0Jia>~g=ci^P7Kej zX21l8_mz>WjvCk*vmhm^w*k=6$r35R0c4p6ySI{wA(?o`S;~aZqBh5{8z_BwI|CMl zfdS&MdoBuO0df_y9uOF#yD^9cgU^-qZQ=>5xWgzqz#E24aS+(*5WW&-P8}Sq1uzEU z3>jk~uqUrT2H7m(Ehrp9q$cdkPc^gwJ{_KrpbS7Y{*?!97~Rqx!$D9B@9=7>sSuC^ zmHmi18tTKX(0K$|zKgHVkumGxD|nEJRFdK40d{mYag=i?xF)oa3Xizp)hObac{yl> zv6`Tru)@?955V*gIOsMIw`me_^A=NzVZdA&5A51ig6<6jR3z*MxAtDafE`9Fq8<$eGF literal 0 HcmV?d00001 diff --git a/cst337/lec/lec10.md b/cst337/lec/lec10.md index 7fd6d5e..4fc3406 100644 --- a/cst337/lec/lec10.md +++ b/cst337/lec/lec10.md @@ -1,4 +1,32 @@ # lec10 -> whole section still needs to be transcribed over fom paper +## Half-adder + +This will be the building block for adding bit-strings together later on however, for now we are going to just add two singular bits. +To accomplish this we'll build a half adder. + +This means our logic circuit must adhere to the following logic table. +If both inputs are 0 then our result is 0 and we don't have to carry anything out. +If only one input A/B is 1 then our result will clearly be 1 and our carry will be 0. +Finally if both inputs are 0 then since we can't fit 2 in a single bit it means we have to carry-out a 1, and our result will be 0. + +With all of this in mind we have a table to guide how we will implement our logic circuit. +I __highly__ suggest that you try to build a logic circuit on your own first as most of the content is best learned through practice. + +| A | B | Carry-out | Result | +|---|---|---|---| +| 0 | 0 | 0 | 0 | +| 0 | 1 | 0 | 1 | +| 1 | 0 | 0 | 1 | +| 1 | 1 | 1 | 0 | + +![fig0](../img/fig0lec10.png) + +## Full Adder + +If we only want to add single-bit's then a half-adder works fine but if we want to add multiple bits say `1011 + 0010` then we need to consider that we will likely have to chain these together. +The full-adder has 1 main difference from the half-adder, it has 3 inputs, 2 main inputs and 1 input for the carry bit. +The carry bit will propagate along the operation now if we chain these together, _just like real addition_! + +![fig1](../img/fig1lec10.png)