Lecture 5:Machine LanguageCS442: Great Insights in Computer ScienceMichael L. Littman, Spring 2006Recap• Using logic gates, we know how to do a bunch of things with bits:• add• test equality• if-then-else gate• select one bit from a set (universal gate)What Can We Do?• Lots: Any function of bits, we can specify with logic gates.• But, creating dedicated circuitry for every new problem is daunting and inefficient.• Would like a way of using a fixed set of circuits to act like any circuitry we might want.• Trade gates for time...Recipe for squaresx takes on the value of the first 11 squaresx = 0y = 1z = 2for i in range(0,11):x = x + yy = y + zList of Squaresixyz00121132245239724169252511263613274915286417298119210100212“=” means “assignment”Memory• Need a place to store the various quantities we’re working with.• Main memory is like a giant filing cabinet, where each drawer is numbered consecutively and can store one byte.• Need to be able to store and retrieve values.Memory Circuitaddressmem[0] ... mem[21] ... mem[63]Content of mem[21] if address = 21 (010101)Otherwise, FFFFFFFF[F, T, F, T, F, T]EQUAL6IFTHENELSE8[F, F, F, F, F, F, F, F]Similar circuits for the other 63 locations.64-byte-inputbitwise ORContent of mem[address] • Let’s say there are 64 memory locations, 0-255.• Each one has an 6-bit name called its “address”.• Memory circuit takes the contents of memory (64 x 8 bits) and an address, 518 bits in all, & outputs the byte stored at the corresponding address.Memory Lookupdef memlookup(add, mem): mem00 = mem[0] mem01 = ifthenelse8(equal8(intToByte( 1),add), mem[ 1], mem00) mem02 = ifthenelse8(equal8(intToByte( 2),add), mem[ 2], mem01) mem03 = ifthenelse8(equal8(intToByte( 3),add), mem[ 3], mem02) mem04 = ifthenelse8(equal8(intToByte( 4),add), mem[ 4], mem03) mem05 = ifthenelse8(equal8(intToByte( 5),add), mem[ 5], mem04) mem06 = ifthenelse8(equal8(intToByte( 6),add), mem[ 6], mem05) mem07 = ifthenelse8(equal8(intToByte( 7),add), mem[ 7], mem06) mem08 = ifthenelse8(equal8(intToByte( 8),add), mem[ 8], mem07) mem09 = ifthenelse8(equal8(intToByte( 9),add), mem[ 9], mem08) mem10 = ifthenelse8(equal8(intToByte(10),add), mem[10], mem09) mem11 = ifthenelse8(equal8(intToByte(11),add), mem[11], mem10) mem12 = ifthenelse8(equal8(intToByte(12),add), mem[12], mem11) mem13 = ifthenelse8(equal8(intToByte(13),add), mem[13], mem12) mem14 = ifthenelse8(equal8(intToByte(14),add), mem[14], mem13) mem15 = ifthenelse8(equal8(intToByte(15),add), mem[15], mem14) mem16 = ifthenelse8(equal8(intToByte(16),add), mem[16], mem15) mem17 = ifthenelse8(equal8(intToByte(17),add), mem[17], mem16) mem18 = ifthenelse8(equal8(intToByte(18),add), mem[18], mem17) mem19 = ifthenelse8(equal8(intToByte(19),add), mem[19], mem18) mem20 = ifthenelse8(equal8(intToByte(20),add), mem[20], mem19) mem21 = ifthenelse8(equal8(intToByte(21),add), mem[21], mem20) mem22 = ifthenelse8(equal8(intToByte(22),add), mem[22], mem21) mem23 = ifthenelse8(equal8(intToByte(23),add), mem[23], mem22) mem24 = ifthenelse8(equal8(intToByte(24),add), mem[24], mem23) mem25 = ifthenelse8(equal8(intToByte(25),add), mem[25], mem24) mem26 = ifthenelse8(equal8(intToByte(26),add), mem[26], mem25) mem27 = ifthenelse8(equal8(intToByte(27),add), mem[27], mem26) mem28 = ifthenelse8(equal8(intToByte(28),add), mem[28], mem27) mem29 = ifthenelse8(equal8(intToByte(29),add), mem[29], mem28) mem30 = ifthenelse8(equal8(intToByte(30),add), mem[30], mem29) mem31 = ifthenelse8(equal8(intToByte(31),add), mem[31], mem30) mem32 = ifthenelse8(equal8(intToByte(32),add), mem[32], mem31) mem33 = ifthenelse8(equal8(intToByte(33),add), mem[33], mem32) mem34 = ifthenelse8(equal8(intToByte(34),add), mem[34], mem33) mem35 = ifthenelse8(equal8(intToByte(35),add), mem[35], mem34) mem36 = ifthenelse8(equal8(intToByte(36),add), mem[36], mem35) mem37 = ifthenelse8(equal8(intToByte(37),add), mem[37], mem36) mem38 = ifthenelse8(equal8(intToByte(38),add), mem[38], mem37) mem39 = ifthenelse8(equal8(intToByte(39),add), mem[39], mem38) mem40 = ifthenelse8(equal8(intToByte(40),add), mem[40], mem39) mem41 = ifthenelse8(equal8(intToByte(41),add), mem[41], mem40) mem42 = ifthenelse8(equal8(intToByte(42),add), mem[42], mem41) mem43 = ifthenelse8(equal8(intToByte(43),add), mem[43], mem42) mem44 = ifthenelse8(equal8(intToByte(44),add), mem[44], mem43) mem45 = ifthenelse8(equal8(intToByte(45),add), mem[45], mem44) mem46 = ifthenelse8(equal8(intToByte(46),add), mem[46], mem45) mem47 = ifthenelse8(equal8(intToByte(47),add), mem[47], mem46) mem48 = ifthenelse8(equal8(intToByte(48),add), mem[48], mem47) mem49 = ifthenelse8(equal8(intToByte(49),add), mem[49], mem48) mem50 = ifthenelse8(equal8(intToByte(50),add), mem[50], mem49) mem51 = ifthenelse8(equal8(intToByte(51),add), mem[51], mem50) mem52 = ifthenelse8(equal8(intToByte(52),add), mem[52], mem51) mem53 = ifthenelse8(equal8(intToByte(53),add), mem[53], mem52) mem54 = ifthenelse8(equal8(intToByte(54),add), mem[54], mem53) mem55 = ifthenelse8(equal8(intToByte(55),add), mem[55], mem54) mem56 = ifthenelse8(equal8(intToByte(56),add), mem[56], mem55) mem57 = ifthenelse8(equal8(intToByte(57),add), mem[57], mem56) mem58 = ifthenelse8(equal8(intToByte(58),add), mem[58], mem57) mem59 = ifthenelse8(equal8(intToByte(59),add), mem[59], mem58) mem60 = ifthenelse8(equal8(intToByte(60),add), mem[60], mem59) mem61 = ifthenelse8(equal8(intToByte(61),add), mem[61], mem60) mem62 = ifthenelse8(equal8(intToByte(62),add), mem[62], mem61) mem63 = ifthenelse8(equal8(intToByte(63),add), mem[63], mem62) return mem63Writing to Memoryaddressmem[0] ... mem[21] ... mem[63]Content of newval if address = 21 (010101)Otherwise, mem[21] (no change)[F, T, F, T, F, T]EQUAL6IFTHENELSE8Similar circuits for the other 63 locations.newvalmem[0] ... mem[21] ... mem[63]• Similar circuit allows memory cells to be altered.• mem[address] = newval• If needed for future processing, copied back up at the end of the cycle.Memory Writedef memwrite(active, add, mem, val): return [