ENGR 303 Introduction to Logic Design Lecture 7. Dr. Chuck Brown Engineering and Computer Information Science Folsom Lake College
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1 Introduction to Logic Design Lecture 7 Dr. Chuck Brown Engineering and Computer Information Science Folsom Lake College
2 Outline for Todays Lecture Shifter Multiplier / Divider Memory <2>
3 Shifters Logical shifter: shifts value to left or right and fills empty spaces with 0 s Ex: >> 2 = Ex: << 2 = Arithmetic shifter: same as logical shifter, but on right shift, fills empty spaces with the old most significant bit (msb). Ex: >>> 2 = Ex: <<< 2 = Rotator: rotates bits in a circle, such that bits shifted off one end are shifted into the other end Ex: ROR 2 = Ex: ROL 2 = <3> 5-<3>
4 Shifters Logical shifter: Ex: >> 2 = Ex: << 2 = Arithmetic shifter: Ex: >>> 2 = Ex: <<< 2 = Rotator: Ex: ROR 2 = Ex: ROL 2 = <4>
5 Shifter Design A 3 A 2 A 1 A 0 shamt 1: S 1: Y 3 shamt 1:0 A 3:0 >> Y 3: S 1:0 Y S 1:0 10 Y S 1:0 10 Y 0 11 <5>
6 Shifters as Multipliers, Dividers A << N = A 2 N Example: << 2 = (1 2 2 = 4) Example: << 2 = ( = -12) A >>> N = A 2 N Example: >>> 2 = (8 2 2 = 2) Example: >>> 2 = ( = -4) <6>
7 Multipliers Partial products formed by multiplying a single digit of the multiplier with multiplicand Shifted partial products summed to form result Decimal 230 x multiplicand multiplier partial products result + Binary 0101 x x 42 = x 7 = 35 <7>
8 4 x 4 Multiplier A B 4 x 4 P 8 A 3 A 2 A 1 A 0 B 0 B 1 0 A 3 A 2 A 1 A 0 0 x B 3 B 2 B 1 B 0 B 2 A 3 B 0 A 2 B 0 A 1 B 0 A 0 B 0 A 3 B 1 A 2 B 1 A 1 B 1 A 0 B 1 0 A 3 B 2 A 2 B 2 A 1 B 2 A 0 B 2 B 3 + A 3 B 3 A 2 B 3 A 1 B 3 A 0 B 3 P 7 P 6 P 5 P 4 P 3 P 2 P 1 P 0 0 P 7 P 6 P 5 P 4 P 3 P 2 P 1 P 0 <8>
9 0 1 4 x 4 Divider 0 B 3 0 B 2 0 B 1 A 3 B 0 Legend R B Q 3 1 R B C out C in D N R' C out + D C in A 2 N Q 2 Q 1 Q 0 R 3 R 2 R 1 A 1 A 0 R R' A/B = Q + R/B Algorithm: R = 0 for i = N-1 to 0 R = {R << 1. A i } D = R - B if D < 0, Q i =0, R =R else Q i =1, R =D R =R <9>
10 Memory Arrays Efficiently store large amounts of data 3 common types: Dynamic random access memory (DRAM) Static random access memory (SRAM) Read only memory (ROM) M-bit data value read/ written at each unique N-bit address Address N Array M Data <10>
11 Memory Arrays 2-dimensional array of bit cells Each bit cell stores one bit N address bits and M data bits: 2 N rows and M columns Depth: number of rows (number of words) Width: number of columns (size of word) Array size: depth width = 2 N M Address N Array M Data Address Data Address 2 Array depth Data width <11>
12 Memory Array Example bit array Number of words: 4 Word size: 3-bits For example, the 3-bit word at address 10 is 100 Address Data Address 2 Array depth Data width <12>
13 Memory Arrays Address word x 32-bit Array 32 Data <13>
14 Memory Array Bit Cells wordline bit bitline bitline = bitline = wordline = 1 wordline = 0 bitline = bitline = wordline = 1 wordline = 0 (a) (b) <14>
15 Memory Array Bit Cells bitline wordline bit bitline = 0 bitline = Z wordline = 1 wordline = 0 bitline = 1 bitline = Z wordline = 1 wordline = 0 (a) (b) <15>
16 Memory Array Wordline: like an enable single row in memory array read/written corresponds to unique address only one wordline HIGH at once 2:4 Decoder bitline 2 bitline 1 bitline 0 11 wordline 3 Address 2 10 wordline 2 01 wordline 1 00 wordline 0 Data 2 Data 1 Data 0 <16>
17 Types of Memory Random access memory (RAM): volatile Read only memory (ROM): nonvolatile <17>
18 RAM: Random Access Memory Volatile: loses its data when power off Read and written quickly Main memory in your computer is RAM (DRAM) Historically called random access memory because any data word accessed as easily as any other (in contrast to sequential access memories such as a tape recorder) <18>
19 ROM: Read Only Memory Nonvolatile: retains data when power off Read quickly, but writing is impossible or slow Flash memory in cameras, thumb drives, and digital cameras are all ROMs Historically called read only memory because ROMs were written at manufacturing time or by burning fuses. Once ROM was configured, it could not be written again. This is no longer the case for Flash memory and other types of ROMs. <19>
20 Types of RAM DRAM (Dynamic random access memory) SRAM (Static random access memory) Differ in how they store data: DRAM uses a capacitor SRAM uses cross-coupled inverters <20>
21 Memory Arrays Review 2:4 Decoder bitline 2 bitline 1 bitline 0 11 wordline 3 Address wordline 2 wordline 1 wordline 0 Data 2 Data 1 Data 0 DRAM bit cell: SRAM bit cell: bitline bitline bitline wordline wordline <21>
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