Lecture17.pdf

Homework • Reading – Tokheim, Chapter 3, 4, and 6.1 - 6.3 • Labs – Continue in labs with your assigned section 1 Combining Basic Logic Gates • • • • • • • Decoders Encoders Selectors - Multiplexers ALUs Control Units Buses Simple computers 2 Binary Decoder • Logic with n input lines and 2n o...

Homework • Reading – Tokheim, Chapter 3, 4, and 6.1 - 6.3 • Labs – Continue in labs with your assigned section 1 Combining Basic Logic Gates • • • • • • • Decoders Encoders Selectors - Multiplexers ALUs Control Units Buses Simple computers 2 Binary Decoder • Logic with n input lines and 2n output lines • Only one output is a 1 for any given input n inputs Binary Decoder 2n outputs 3 Building a Binary Decoder • Start with a 2-bit decoder: X0 X1 AND Y0 AND Y1 AND Y2 AND Y3 X0 0 0 1 1 X1 Y 0 Y0=1 1 Y1=1 0 Y2=1 1 Y3=1 Enable 4 Then Add Two to Make Three... X0 X1 X2 2-bit Decoder Y0 Y1 Y2 Y3 NOT 2-bit Decoder Y4 Y5 Y6 Y7 5 Developing an Encoder • If we can decode, then we need to encode • Encode from 1 out of n into a binary weighted form • A keyboard encoder does this X0 X1 X2 X3 X4 ... X7 NC OR Y0 OR Y1 OR Y2 6 Next Comes a Selector • Like a switch; also called a multiplexer or MUX S1 S2 a b c MUX or Selector y d • Again, build it up from simple basic logic gates 7 A 1-bit Selector S1 S2 Decoder a b c d AND AND O R AND y AND 8 A 4-bit Selector S S0 S1 A a0 b0 c0 d0 B Y0 Y1 D S A B Y3 Y C Y2 a3 b3 c3 d3 MUX C D 2 4 4 4 MUX 4 Y 4 9 The ALU Is Next • Logical and arithmetic operations • Variations in – Base • Binary • Decimal • BCD (binary coded decimal) A Control Signals B ALU CCs – Implementation • Serial • Parallel • Pipelined f(A,B) 10 Simple Example - Binary Adder • Develop a half-adder (HA) • Use two HA’s to build a full-adder (FA) 11 The Half-Adder and or not Sum = (a • b) + (a • b ) = (a + b ) • (a + b) Carry = a • b a b a b HA Sum Cout XOR Sum AND Cout a b 0 0 1 1 0 1 0 1 Sum Carry 0 1 1 0 0 0 0 1 12 From HA to FA Truth table for FA a b cin a b b cin Sum 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 Cout Sum Full Adder cout Cout Half Adder sum cin a Half Adder XOR Cout 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 Cout Sum 13 Using Full Adders for 2-bit Addition 0 a0 b0 C0 a1 b1 00 + 11 (0) 1 1 Full Adder Full Adder 00 +01 (0) 0 1 Sum0 C0 Sum1 C1 11 11 +01 +1 1 (1) 0 0 (1) 1 0 Note: The carry flag value after the addition represents the N+1 bit value in the result a b Cin Sum0 C0 LSB 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 MSBs 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 Cn-1 Sumn Cn 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 14 Using Full Adders for Subtraction Difference = a =a =a =a 1 a0 ~b0 C0 a1 ~b1 (1) 0 0 - 11 01 Full Adder Full Adder 00 +01 (0) 0 1 - b + (-b) + (~b + 1) + ~b + 1 Sum0 C0 Sum1 C1 (0)1 1 -01 10 11 +1 1 (1) 1 0 Note: The carry flag value after the ~ and addition is the opposite of the subtract borrow condition a ~b C0 Sum C1 LSB 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 MSBs 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 Cn-1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 Cn 0 0 0 1 0 1 1 1 15 Configurable Add/Subtract ALU Subtract/Add # From Instruction Decoding Logic (0 for add 1 for subtract) a0 b0 . . . bn-1 Full Adder XOR . . . XOR C0 Cn-2 an-1 . . . Full Adder EFlags Register Sum0 . . . NOR Sumn-1 Cn-1 XOR Zero Flag Sign Flag Overflow Flag = Cn-2*Cn-1# Carry Flag 16