CS计算机代考程序代写 mips Abstraction & Digital Logic: From Transistors to Gates

Abstraction & Digital Logic: From Transistors to Gates

Four-Way Multiplexer
 n-bit selector and 2n inputs, one output
 output equals one of the inputs, depending on
selector
 “Four-to-one mux”
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Two-to-Four Decoder
 n inputs, 2n outputs
 exactly one output is 1 for each possible input pattern
 Uses:
 Convert memory or register address to a control line
 Convert an opcode to one of n control lines
 We will get to this in the MIPS material
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Two-to-Four Decoder
 n inputs, 2n outputs
 exactly one output is 1 for each possible input pattern
 Uses:
 Convert memory or register address to a control line
 Convert an opcode to one of n control lines
 We will get to this in the MIPS material
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Time for some…
 We currently use decimal system in daily life
(deci=10 digits,0-9)
 We know..
1+0=1 1+1=2;1+2=3;1+3=4… 1+8=9;
 What is 1+9=?? CSE12 Winter 2021
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Intro to Addition in Binary Base
 010+110=110
 110+110 =210
 110 + 210 = 310

 02+12=12  12+12=102
 112+12 =1002

…..
 110 + 910 = 1010
…..
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Binary Addition and Half-Adder
 02 + 02 = 02
 02 + 12 = 12
 12 + 02 = 12
 12 +12 =102
 …
 A half-adder can add 2 bits and produces a sum and carry signal
 Sum = A xor B  Carry = AB
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One-Bit Full Adder
A B Cin Cout S
000 001 010
011 100 101 110 111
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Four-Bit Full Adder
Ripple-carry adder
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Masking
 Want to look only at certain bits of a binary word
 Use a mask to remove the uninteresting bits
 Example:
 Two values: 01001101 and 01001001
 If we want to see bit 3 from right, we AND it with 00000100 to get
00000100 and 00000000, respectively.
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Logic Minimization
ABC
000
001
010
011
100
101
110
111
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0
0
1
1
1
0
1
0
Start with SOP:
A’BC’ + A’BC + AB’C’ + ABC’
Factor A’ and A out:
A’(BC’ + BC) + A(B’C’ + BC’)
Factor B and C’ out:
A’(B(C’ + C)) + A(C’(B’ + B))
Use identity that C’+C=1 and B’+B=1: A’B + AC’
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Motivation between logic minimization
 Original form:  Simplified form:
A’BC’ + A’BC + AB’C’ + ABC’
A’B + AC’
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Wave Diagram concept
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Building functions from logic gates
 Combinational Logic Circuit
 Output depends only on the current inputs  Stateless (memoryless)
 Sequential Logic Circuit
 Output depends on the sequence of inputs (past
and present)
 Stores information (state) from past inputs
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Sequential Circuits and Memory

Combinational vs. Sequential
■ Combinational circuit
◆ Always gives the same output for a given set of
■ Sequential circuit
◆ Remembers previous input
◆ Output depends on state and input
inputs
◆ Example: Adder always generates sum and carry, regardless of previous inputs
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Sequential Circuits
■ Store information
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Reset-Set (RS) Latch – NAND SR Latch
■ Two inputs: Set and Reset
■ Setto0oneofthetwoinputsatatimetostore
a value, S sets, R clears
■ The transition to 00 generates an undefined output
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NAND SR Latch
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R-S Latch Nor Gates
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