Computer Structure - The ALU Goal: Build an ALU  The Arithmetic Logic Unit or ALU is the device that performs arithmetic and logical operations in the computer.  We will build it out of 4 basic building blocks.  AND gate: performs the AND operation on 2 signals.  OR gate: performs the OR operation on 2 signals.  Inverter: inverts the incoming signal (o to 1, 1 to 0).  Multiplexor: chooses between one out of several incoming signals. 1/13

The Basic Building Blocks 2/13

1-bit Full Adder  1-bit addition has 3 inputs (a, b, CarryIn) and 2 outputs (Sum, CarryOut).  The CarryOut is set if at least 2 out of a, b, and CarryIn are 1.  The Sum is set when exactly one input is 1 or all three are 1. 3/13

Computer Structure - The ALU 1-bit ALU  We now have a 1-bit ALU that can perform AND, OR and addition.  All 3 operations are performed in parallel.  The MUX (Multiplexor), dependent on the operation, chooses the result. 4/13

Computer Structure - The ALU Subtraction  Subtraction is performed by adding the negative value.  Thus we have to add an inverter.  A MUX has to be added to choose between addition and subtraction. 5/13

Computer Structure - The ALU 32-bit ALU  With 32 of these 1-bit ALUs we can build a 32- bit ALU.  The CarryOut of the Nth 1-bit ALU is connected to the CarryIn of the N+1 1-bit ALU.  This adder is called a ripple carry or ripple adder.  A single carry out in the least significant bit (LSB) can cause a carry out of the MSB. 6/13

Computer Structure - The ALU Adding the slt instruction  slt produces 1 if rs = rt.  Thus slt will set all but the LSB to 0 with the LSB being dependent on the result.  We add a new input to the multiplexor called Less, this will be the output of slt.  To set the LSB we perform rs - rt.  If the result is negative we must set the output. Thus the sign bit is the correct output.  But it isn't the output of slt (Less is) so a new output is added to the 1-bit ALU of the MSB, Set.  The input of the last 31 Less lines is 0, the input of the 1st Less line is Set of the 32nd ALU. 7/13

ALU with slt  The Less line is added to all ALUs.  The 32nd ALU has a Set line.  The 32nd ALU also has overflow detection circuitry. 8/13

Computer Structure - The ALU The New ALU  All the Less inputs are hardwired to zero.  Except the LSB Less input which is wired to the Set output of the MSB 1-bit ALU. 9/13

Computer Structure - The ALU Comparison in the ALU  bne and beq compare 2 numbers.  a is equal to b if a - b=0.  The output line Zero is set to 1 if all the Result lines are 0.  This happens if a == b. 10/13

Computer Structure - The ALU ALU Summary  Our ALU can perform AND, OR, Addition, Subtraction, Set on less then (slt), and Equality tests. The universal symbol of the ALU is shown here: 11/13

Computer Structure - The ALU Fast Addition  The addition we have just described is to slow. We have to wait until carry values ripple through the ALU.  Do we have to wait? c1 = (b0*c0)+(a0*c0)+(a0*b0) c2 = (b1*c1)+(a1*c1)+(a1*b1)  Thus we can compute c2 without waiting for the carry c1: c2=(a1*a0*b0)+(a1*a0*c0)+(a1*b0*c0)+(b1*a0*b0)+(b1*a0*c0)+(b1*b0*c 0)+(a1*b1)  We can in fact compute c32 with only a,b and c0. However the size of the adder will be very large. This is called a Fast-Adder. 12/13

Computer Structure - The ALU Carry Lookahead Addition  Each 4 bit Fast-Adder outputs a Propagate (תעביר) and Generate (תייצר) bit.  Generate means there is a CarryOut, independent of the CarryIn..  Propagate means the CarryOut is dependent on the CarryIn.  This is called Carry Lookahead Addition. 13/13