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ECE 3110: Introduction to Digital SystemsChapter 6Combinational Logic Design Examples Barrel Shifter Speical purpose Encoders/Comparators
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HW solutions Ex. 5.46 Ex. 5.19
Design examples using combinational building blocks (decoders, encoders, multiplexers, comparators, three-state devices, adders). • Barrel shifter • Dual-priority encoder • Cascading comparators, mode-dependent comparator
Barrel shifter design example • n data inputs, n data outputs • Control inputs specify number of positions to rotate or shift data inputs • Example: n = 16 • DIN[15:0], DOUT[15:0], S[3:0] (shift amount) • Many possible solutions, all based on multiplexers
Multiplexers (mux) Eg. Put between Processor’s registers and ALU A 16-bit processor where 3-bit field specifies on of 8 registers. The 3-bit field is connected to the select inputs of an 8-input, 16-bit mux. Select one of n sources of data to transmit on a bus.
16-to-1 barrel shifter 16-to-1 mux = 2 x 74x151 8-to-1 mux + NAND gate
4 16-bit 2-to-1 muxes 16-bit 2-to-1 mux = 4 x 74x157 4-bit 2-to-1 mux
Dual-Priority Encoder • A priority encoder identifies not only the highest but also the second-highest-priority asserted signal among a set of 8 request inputs.
Single-priority encoder 0 1 0 0 1 0 0 1
0 1 0 0 1 0 0 1
Parallel Cascading Comparators • 74x85: serial cascading scheme, delay of propagating the cascading signals through a cascade of comparators. • 74x682: Parallel approach, used to build very wide comparators. • Build 24-bit comparator, using 3 74x682 • PEQQ=EQ2.EQ1.EQ0 • PGTQ=GT2+EQ2.GT1+EQ2.EQ1.GT0
8 bit Comparator +5V 74x85 74x85 A<B A<BIN A<BOUT A<BIN A<BOUT A=B A=BIN A=B OUT A=BIN A=B OUT A>B A>BIN A>BOUT A>BIN A>BOUT A0 A0 A4 A0 B0 B0 B4 B0 A1 A1 A5 A1 B1 B1 B5 B1 A2 A2 A6 A2 B2 B2 B6 B2 A3 A3 A7 A3 B3 B3 B7 B3 Least Significant bits Most Significant bits
Mode-dependent Comparator • Design a c.c. whose inputs are two 8-bit unsigned binary integers(X,Y), and a control signal(MIN/MAX). The output is an 8-bit unsigned binary integer Z, such that • Z=min(X,Y) if MIN/MAX=1; • Z=max(X,Y) otherwise
Next… • Sequential Logic Introduction