逻辑回路 Unit1.ppt

Unit 1Number Systems and Conversion Analog vs. Digital Systems Analog Systems: The physical quantities vary continuously. Accuracy and repeatability/reliability are limited. (infinite number of digits below decimal point) (analogous to mercury thermometer ) Digital Systems: The physical quantities are discrete values. Accurate to the resolution and repeatable. (limited by the number of bits) (analogous to brick layers) Digital Systems Design System design: Break down the system into subsystems, and specify the characteristics of each subsystem. (CPU, memory, I/O etc.) Logic design: Determine how to interconnect basic logic building blocks to perform a specific function. (interconnect Gates, Flip-flops to form an ADDER) Circuit design: Specify the interconnection of specific components. (resistors, diodes, transistors to form a gate, flip-flops etc.) Switching Circuit Combinational circuit: Output values depend only on the present input values. Sequential circuit: Output values depend on both the present and past input values. (said to have memory) Number Systems and Conversion Base 10 (Decimal) 953.7810 = (9x102) + (5x101) + (3x100) + (7x10-1) + (8x10-2) = 900 + 50 + 3 + 7/10 + 8/100 Base 2 (Binary) 1011.112 = (1x23) + (0x22) + (1x21) + (1x20) + (1x2-1) + (1x2-2) = 8 + 0 + 2 + 1 + ? + ? = 11.7510 Number Systems and Conversion Base 8 (Octal) 147.38 = (1x82) + (4x81) + (7x80) + (3x8-1 ) = 64 + 32 + 7 + 0.375 = 103.37510 Base 16 (Hexadecimal) A2F16 = (10x162) + (2x161) + (15x160) = 2560 + 32 + 15 = 260710 *** Letter ‘A’ to ‘F’ for 10 to 15 Number Systems and Conversion Conversion of a decimal integer to base R using successive division by R N = (an an-1 · · · a0 )R = anRn + an-1Rn-1 + · · · + a1R1 +