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1 Pertemuan 21 Arithmetic: I Matakuliah: T0324 / Arsitektur dan Organisasi Komputer Tahun: 2005 Versi: 1
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2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Membandingkan berbagai jenis operasi aritmatika didalam sistem komputer digital ( C4 ) ( No TIK : 10 )
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3 Chapter 6. Arithmetic: I (OFC5)
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4 s i = c i +1 = Figure 6.1. Logic specification for a stage of binary addition. 13 7 +Y 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Example: 1 0 ==0 0 1 1 1 1 1 0 0 1 1110 Legend for stagei x i y i Carry-inc i Sums i Carry-outc i+1 X Z + 6 0 + x i y i s i Carry-out c i+1 Carry-in c i x i y i c i x i y i c i x i y i c i x i y i c i x i y i c i = +++ y i c i x i c i x i y i ++
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7 Figure 6.8. Sign extension of negative multiplicand. 1 0 1111110011 110 110 1 0 1000111011 000000 1100111 00000000 110011111 13- 143- 11+ () Sign extension is shown in blue
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8 Figure 6.9. Normal and Booth multiplication schemes. 0 1 0 00 101101 0 000000 1 0 011010 1011010 1011010 1011010 0000000 000000 011000101010 010111 0000 00000000000000 0 00 111111101001 00 0 000101101 00000000 01100010010001 2's complement of the multiplicand 0 0 0 0 1+1- 1+1+1+1+ 0 0 0000000000 00000000 0000000
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9 Figure 6.10. Booth recoding of a multiplier. 001101011100110100 00000000 1+1-1-1+1-1+1-1+1-1+
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10 Figure 6.11. Booth multiplication with a negative multiplier. 01 0 1111011 000000000 00 0110 0000110 1100111 000000 0100011111 1 101101 11010 6- 13+() 78- +11-1-
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11 Multiplier Biti i 1 - Version of multiplicand selected by biti 0 1 0 0 01 11 0M 1+M 1 M 0M Figure 6.12. Booth multiplier recoding table.
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12 Figure 6.13. Booth recoded multipliers. 1 0 1110000111110000 001111011010001 101010101010101 0 000000000000 00000000 1-1-1-1-1-1-1-1- 1-1-1-1- 1-1- 1+1+1+1+1+1+1+1+ 1+ 1+1+1+ 1+ Worst-case multiplier Ordinary multiplier Good multiplier
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13 Pertemuan 22 Arithmetic: II Matakuliah: T0324 / Arsitektur dan Organisasi Komputer Tahun: 2005 Versi: 1
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14 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Membandingkan berbagai jenis operasi aritmatika didalam sistem komputer digital ( C4 ) ( No TIK : 10 )
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15 Chapter 6. Arithmetic: II (OFC6)
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17 Figure 6.16. Ripple-carry and carry-save arrays for the multiplication operation M Q = P for 4-bit operands.
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18 Figure 6.17. A multiplication example used to illustrate carry-save addition as shown in Figure 6.18. 100111 100111 100111 111111 100111 M Q A B C D E F (2,835) X (45) (63) 100111 100111 100111 000111111000 Product
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19 Figure 6.19. Schematic representation of the carry-save addition operations in Figure 6.18.
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20 Figure 6.20. Longhand division examples. 1101 1 13 14 26 21 274100010010 10101 1101 1 1110 1101 10000 13 1101
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21 q n1- m n1- -bit Divisor M Control sequencer Dividend Q Shift left adder a n1- a 0 q 0 m 0 a n 0 Add/Subtract Quotient setting n1+ Figure 6.21. Circuit arrangement for binary division. A
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22 0110010000101 (a) Unnormalized value (b) Normalized version 0 100010000010110... (There is no implicit 1 to the left of the binary point.) Value represented 0.0010110 2 9 +=... Value represented1.0110 2 6 += Figure 6.25. Floating-point normalization in IEEE single-precision format. excess-127 exponent
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23 RepresentationExamples Sign and magnitude 9's complement 10's complement 0526 9473 9474 0070 9929 9930 Figure P6.1. Signed numbers in base 10 used in Problem 6.3. +526 526+70 70
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24 12 bits 5 bits excess-15 exponent 6 bits fractional mantissa 1 bit for sign of number Figure P6.2. Floating-point format used in Problem 6.25. + 0 signifies -1 signifies
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25 Figure P6.3. 1's-complement addition used in Problem 6.36. (3)1 0 1 0 0 0 0 1 1 0 0 1 1110 +(+0 0 1110 3 (6)1 0 1 0 0 1 1 1 0 0 0 0 0001 +(+1 1 0011 5 - ) 2- 3-)
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