Chapter 4 Register Transfer and MicrooperationsOutlineSlide 3Arithmetic MicrooperationsSlide 5Slide 6BINARY ADDERSlide 8Slide 9Full AdderSlide 11Slide 12BINARY ADDER-SUBTRACTORSlide 14Slide 15Slide 164.5 Logic MicrooperationsSlide 18ExampleMore Logic MicrooperationHomework 1Slide 224-6 Shift MicrooperationsShift MicrooperationsLogical ShiftLogical Shift ExampleCircular ShiftCircular Shift ExampleArithmetic ShiftArithmetic Shift RightSlide 31Arithmetic Shift LeftSlide 33Slide 34ExampleChapter 4 Register Transfer and MicrooperationsDr. Bernard Chen Ph.D.University of Central ArkansasSpring 2010Outline•Microoperations •Arithmetic microoperation•Logic microoperation•Shift microoperationBuss1s2s016-bit common busClockLDLDLDINROUTRIRINPRLDINRCLRLDINRCLRLDINRCLRLDINRCLRWRITEAddressAdder & LogicEDRPCARCLR7123456Computer System Architecture, Mano, Copyright (C) 1993 Prentice-Hall, Inc. ACMano’s Computer Figure 5-4READMemory Unit 4096x16TRArithmetic MicrooperationsA Microoperation is an elementary operation performed with the data stored in registers.Usually, it consist of the following 4 categories:•Register transfer: transfer data from one register to another•Arithmetic microoperation•Logic microoperation•Shift microoperationArithmetic MicrooperationsSymbolic designation Description R3 ← R1 + R2 Contents of R1 plus R2 transferred to R3 R3 ← R1 – R2 Contents of R1 minus R2 transferred to R3 R2 ← R2 Complement the contents of R2 (1’s complement) R2 ← R2 + 1 2’s Complement the contents of R2 (negate) R3 ← R1 + R2 + 1 R1 plus the 2’s complement of R2 (subtract) R1 ← R1 + 1 Increment the contents of R1 by one R1 ← R1 – 1 Decrement the contents of R1 by oneMultiplication and division are not basic arithmetic operationsMultiplication : R0 = R1 * R2Division : R0 = R1 / R2Arithmetic MicrooperationsA single circuit does both arithmetic addition and subtraction depending on control signals.• Arithmetic addition:R3  R1 + R2 (Here + is not logical OR. It denotes addition)BINARY ADDERBinary adder is constructed with full-adder circuits connected in cascade.•It has 3 input and 2 output To implement an arithmetic adder for multiple-bit inputs, we need to treat the carry out from the lower bit as a third input ( it becomes carry in for the current bit) in addition to the two input bits at the current bit position.FULL-ADDERX1Y1Z1S 1 C1X0Y0Z0S0 C0+Full- Adder It adds 3-bits, it has 3-inputs and 2-outputs We will use x, y and z for inputs and s for sum and c for carry are the two outputs.The truth tablex y z c s0 0 0 0 00 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1C= z (x  y) + xyS= x  y  z Putting them together we get:The logic diagram for the full adderFull AdderBINARY ADDERBinary adder is constructed with full-adder circuits connected in cascade.Arithmetic MicrooperationsArithmetic subtraction:R3 R1 + R2’ + 1where R2 is the 1’s complement of R2.Adding 1 to the one’s complement is equivalent to taking the 2’s complement of R2 and adding it to R1.BINARY ADDER-SUBTRACTOR• The addition and subtraction operations cane be combined into one common circuit by including an exclusive-OR gate with each full-adder.XORM b0 0 0 0 1 11 0 11 1 0BINARY ADDER-SUBTRACTOR=• M = 0: Note that B XOR 0 = B. This is exactly the same as the binary adder with carry in C0 = 0.M = 1: Note that B XOR 1 = B (flip all B bits). The outputs of the XOR gates are thus the 1’s complement of B. M = 1 also provides a carry in 1. The entire operation is: A + B’ + 1.BINARY ADDER-SUBTRACTOROutline•Microoperations •Arithmetic microoperation•Logic microoperation•Shift microoperationManipulating the bits stored in a register Logic Microoperations4.5 Logic 4.5 Logic MicrooperationsMicrooperations• A variety of logic gates are inserted for each bit of registers. Different bitwise logical operations are selected by select signals.LOGIC CIRCUITExample Extend the previous logic circuit to accommodate XNOR, NAND, NOR, and the complement of the second input.S2S1S0Output Operation0 0 0 X  Y AND0 0 1 X  Y OR0 1 0 X  Y XOR0 1 1 A Complement A1 0 0 (X  Y) NAND1 0 1 (X  Y) NOR1 1 0 (X  Y) XNOR1 1 1 B Complement BMore Logic MicrooperationTABLE 4-6. Sixteen Logic Microoperations X Y F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F150 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 11 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 11 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 TABLE 4-5. Truth Table for 16 Functions of Two Variables Boolean function Microoperation Name F0 = 0 F ← 0 Clear F1 = xy F ← A∧B AND F2 = xy’ F ← A∧B F3 = x F ← A Transfer A F4 = x’y F ← A∧B F5 = y F ← B Transfer B F6 = x  y F ← A B Ex-OR F7 = x+y F ← A∨B OR Boolean function Microoperation Name F8 = (x+y)’ F ← A∨B NOR F9 = (x  y)’ F ← A B Ex-NOR F10 = y’ F ← B Compl-B F11 = x+y’ F ← A∨B F12 = x’ F ← A Compl-A F13 = x’+y F ← A∨B F14 = (xy)’ F ← A∧B NAND F15 = 1 F ← all 1’s set to all 1’sHomework 1Design a multiplexer to select one of the 16 previous functions.Outline•Microoperations •Arithmetic microoperation•Logic microoperation•Shift microoperation4-6 Shift MicrooperationsShift Microoperations : Shift microoperations are used for serial transfer of dataThree types of shift microoperation : Logical, Circular, and ArithmeticShift MicrooperationsSymbolic designation Description R ← shl R Shift-left register R R ← shr R Shift-right register R R ← cil R