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EE365 Adv. Digital Circuit Design Clarkson University Lecture #9 Math Units ROMs Topics • • • • Lect #9 Comparators Adders Multipliers ROMs Rissacher EE365 Equality Comparators • 1-bit comparator • 4-bit comparator EQ_L Lect #9 Rissacher EE365 8-bit Magnitude Comparator Lect #9 Rissacher EE365 Other conditions Lect #9 Rissacher EE365 Adders • Basic building block is “full adder” – 1-bit-wide adder, produces sum and carry outputs • Truth table: Lect #9 X Y Cin S Cout 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 Rissacher EE365 Full-adder circuit Lect #9 Rissacher EE365 Ripple adder • Speed limited by carry chain • Faster adders eliminate or limit carry chain – 2-level AND-OR logic ==> 2n product terms – 3 or 4 levels of logic, carry look-ahead Lect #9 Rissacher EE365 74x283 4-bit adder • Uses carry look-ahead internally Lect #9 Rissacher EE365 “generate” “half sum” “propagate” Lect #9 carry-in from previous stage Rissacher EE365 Ripple carry between groups Lect #9 Rissacher EE365 Look-ahead carry between groups Lect #9 Rissacher EE365 Subtraction • Subtraction is the same as addition of the two’s complement. • The two’s complement is the bit-by-bit complement plus 1. • Therefore, X – Y = X + Y + 1 . – Complement Y inputs to adder, set Cin to 1. – For a borrow, set Cin to 0. Lect #9 Rissacher EE365 Full subtractor = full adder, almost Lect #9 Rissacher EE365 Multipliers • 8x8 multiplier Lect #9 Rissacher EE365 Full-adder array Lect #9 Rissacher EE365 Faster carry chain Lect #9 Rissacher EE365 Read-Only Memories Lect #9 Rissacher EE365 Why “ROM”? • Program storage – Boot ROM for personal computers – Complete application storage for embedded systems. • Actually, a ROM is a combinational circuit, basically a truth-table lookup. – Can perform any combinational logic function – Address inputs = function inputs – Data outputs = function outputs Lect #9 Rissacher EE365 Logic-inROM example Lect #9 Rissacher EE365 4x4 multiplier example Lect #9 Rissacher EE365 Internal ROM structure PDP-11 boot ROM (64 words, 1024 diodes) Lect #9 Rissacher EE365 Two-dimensional decoding ? Lect #9 Rissacher EE365 Larger example, 32Kx8 ROM Lect #9 Rissacher EE365 Today’s ROMs • 256K bytes, 1M byte, or larger • Use MOS transistors Lect #9 Rissacher EE365 EEPROMs, Flash PROMs • Programmable and erasable using floating-gate MOS transistors Lect #9 Rissacher EE365 Typical commercial EEPROMs Lect #9 Rissacher EE365 EEPROM programming • Apply a higher voltage to force bit change – E.g., VPP = 12 V – On-chip high-voltage “charge pump” in newer chips • Erase bits – Byte-byte – Entire chip (“flash”) – One block (typically 32K - 66K bytes) at a time • Programming and erasing are a lot slower than reading (milliseconds vs. 10’s of nanoseconds) Lect #9 Rissacher EE365 Microprocessor EPROM application Lect #9 Rissacher EE365 ROM control and I/O signals Lect #9 Rissacher EE365 Next time • Latches • Flip Flops • Clocking Lect #9 Rissacher EE365
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