Combinational ComparatorsExample: 4-bit ComparatorCombinational Shift CircuitsExample: Combinational 8-Bit Right ShifterEECC341 - ShaabanEECC341 - Shaaban#1 Lec # 12 Winter 2001 1-23-2002Combinational Comparators•Comparing two binary inputs A, B each n bits for equality (i.e A = B) is a common operation in computers.•A single output combinational circuit to accomplish this can be constructed using n 2-input XNOR gates for bit-wise comparison plus one n-input AND gate. The output = 1 if A = B•This can also be done by subtraction (A - B) and checking for a zero result using a single n-input NOR gate.•Example: 1-bit comparator: A, B 1-bit each.–The 1-bit comparison requires a single XNOR gateTruth table:A B (A B)’0 0 10 1 01 0 01 1 1Output(A B)’AB1-bit comparatorOutputEECC341 - ShaabanEECC341 - Shaaban#2 Lec # 12 Winter 2001 1-23-2002Example: 4-bit ComparatorComparatorOutputA3B3Compares A = A3 A2 A1 A0 with B = B3 B2 B1 B0 Output = 1 if A = BA2B2A1B1A0B0EECC341 - ShaabanEECC341 - Shaaban#3 Lec # 12 Winter 2001 1-23-2002Combinational Shift Circuits•An n-bit shift circuit (shifter) has a single n-bit data input A, and a single n-bit output R and a number of control inputs to determine the shift amount (0 to n-1).•Possible shift operations include:– Shift left or right:•Arithmetic right shift (the sign bit is shifted in), •logic shift (0 is shifted in)•Rotate left or right.•Example: Original data input A = 11011•Shift left by one : 10110 •Logic shift right by one: 01101•Arithmetic shift right by one: 11101•Rotate left by one: 10111•Combinational shift circuits are usually constructed using a number of levels of multiplexeres.EECC341 - ShaabanEECC341 - Shaaban#4 Lec # 12 Winter 2001 1-23-2002Example: Combinational 8-Bit Right Shifter 10Mux select SABDBasic Building Block 2-to-1 Mux101010101010101010101010101010101010101010101010S2 S1 S0A0A1A2A3A4A5A6A7R0R1R2R3R4R5R6R7•Propagation delay: 2 gate delays per level x 3 levels = 6 gate delays•How many Mux levels for 32-bit shifter? Propagation delay?S2 S1 S0shift amount from 0 to 7Connect to: 0 for logicright shiftor to A7for arithmetic right shiftor to A0 - A6for rotate right{Three levels of Muxes
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