rev0hbh lec4 adder
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7/21/2019 Rev0hbh Lec4 ADDER
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Herman Budi Har ja ST. , MTHerman Budi Har ja ST. , MT
JURUSANJURUSAN TEKNIK MESINTEKNIK MESIN
UNJANIUNJANI
20152015
Penjumlahan bil. biner Mari kita hitung :
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry 1
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Pengurangan bil. biner Mari kita hitung :
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
10 - 1 = 1
Bilangan tak bertanda Bilangan yang tidak memiliki tanda ‘+’ ataupun ‘-’
Contoh :
bilangan 8 bit : 0000000 - 11111111
: 00 - FFH
: 0 – 255
Penjumlah pada bil. tak bertanda dpt mengakibatkanoverflow sehingga dibutuhkan bit carry.
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Bilangan bertanda Bilangan yang memiliki tanda ‘+’ ataupun ‘-’
Bit MSB : tanda ‘+’ ataupun ‘-’
‘0’ : tanda positif, dan
‘1’ : tanda negatif.
Contoh :
+38 = 0 0 1 0 0 1 1 0
-38 = 1 0 1 0 0 1 1 0
+25 = 0 0 0 0 0 0 0 1 1 0 0 1
-25 = 1 0 0 0 0 0 0 1 1 0 0 1
6
Binary, Decimal addition
34
+ 17
------
51
from LSD to MSD:
7+4 = 1; with carry out of 1
to next column
1 (carry) + 3 + 1 = 5.
answer = 51.
Decimal1010112
+ 0000012
---------------
1011002
From LSB to MSB:
1+1 = 0, carry of 1
1 (carry)+1+0 = 0, carry of 1
1 (carry)+0 + 0 = 1, no carry
1 + 0 = 1
0 + 0 = 0
1 + 0 = 1
answer = 1011002
Binary
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Binary Addition, Subtraction (single digit)The rules for binary addition are:
0 + 0 = 0, carry = 0
1 + 0 = 1, carry = 0
0 + 1 = 1, carry = 0
1 + 1 = 0, carry = 1
The rules for binary subtraction are:
0 - 0 = 0, borrow = 0
1 - 0 = 1, borrow = 0
0 - 1 = 1, borrow = 1
1 - 1 = 0, borrow = 0
Multiple digits:
Borrows, Carries from digits to left of current of digit.
Binary subtraction, addition works just the same as decimal addition,
subtraction.
8
SubtractionDecimal
900
- 001
-------
899
0-1 = 9; with borrow of 1
from next column
0 -1 (borrow) - 0 = 9, with
borrow of 1
9 - 1 (borrow) - 0 = 8.
Answer = 899.
Binary
1002
- 0012
-------
0112
0-1 = 1; with borrow of 1
from next column
0 -1 (borrow) - 0 = 1, with
borrow of 1
1 - 1 (borrow) - 0 = 0.
Answer = 0112.
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Definisi
Rangkaian aritmetika d igital dasar
terdiri dari dua macam :
• Adder, atau rangkaian penjumlah, berfungsi
menjumlahkan dua buah bilangan yang telah
dikonversikan menjadi bilangan-bilangan biner
• Subtraktor, atau rangkaian pengurang, yang berfungsi
mengurangkan dua buah bilangan.
•Sebuah rangkaian Adder terdiri dari Half Adder
dan Full Adder .
Half Adder (1-bit)
A B S(um) C(arry)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Half Adder
A B
Sum
Cout
Half Adder menjumlahkan dua buah bit input, dan menghasilkan nilai jumlahan
(sum) dan nilai lebihnya (carry-out).
Half Adder diletakkan sebagai penjumlah dari bit-bit terendah (Least SignificantBit).
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Breaking Down the Truth Table
Notice the Qcolumn (carry line)from the truthtable? Recognize it?It’s an AND!:Q = A • B
INPUTSINPUTS OUTPUTSOUTPUTS
A A BB QQ RR
00 00 00 00
00 11 00 11
11 00 00 11
11 11 11 00
Breaking Down the Truth Table
Notice the Qcolumn (carry line)from the truthtable? Recognize it?It’s an AND!:Q = A • B
INPUTSINPUTS OUTPUTSOUTPUTS
A A BB QQ RR
00 00 00 00
00 11 00 11
11 00 00 11
11 11 11 00
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Circuit Diagram Q = (~A • B) + (A • ~B)
A A A A
BBBB
XOR SymbolThe symbol for the XOR Gate:
A A
BB
Q = AQ = A BB++++
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Re-Writing the Truth Table The XOR circuit delivers
the Sum Lin e (R) ofadding two single digits.
The AND circuitproduces the Car r y Line(Q) .
We’ve just created afundamental circuitcalled a Hal f Adder , which provides thecapability of adding twosingle bit numbers.
INPUTSINPUTS OUTPUTSOUTPUTS
A A BBQQ RR
A A•B•B A B A B
00 00 00 00
00 11 00 11
11 00 00 11
11 11 11 00
++++
Half Adder (1-bit)
A B S(um) C(arry)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
ABC
BABABAS
A
BSum
Carry
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Breaking down the Truth Table “R will be high iff one and exactly one input is high.”
What expression can we use to prove this statement?R = (~A • B) + (A • ~B)
Full Adder
• Sebuah Full Adder menjumlahkan dua bilangan yang telah dikonversikan menjadibilangan-bilangan biner. Masing-masing bit pada posisi yang sama saling dijumlahkan.
• Full Adder sebagai penjumlah pada bit-bit selain yang terendah.
• Full Adder menjumlahkan dua bit input ditambah dengan nilai Carry-Outdaripenjumlahan bit sebelumnya. Output dari Full Adder adalah hasil penjumlahan (Sum)
dan bit kelebihannya (carry-out).
FULLFULL
ADDER ADDER
A A
BB
CCININ
QQCARRYCARRY
RRSUMSUM
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Truth Table for the Full AdderINPUTSINPUTS OUTPUTSOUTPUTS
A A BB CCININ QQCARRYCARRY RRSUMSUM
00 00 00 00 00
00 00 11 00 11
00 11 00 00 11
00 11 11 11 00
11 00 00 00 11
11 00 11 11 00
11 11 00 11 00
11 11 11 11 11
Circuit Diagram for the Full Adder A A
BB
RRSUMSUM
QQCARRYCARRY
CCININ
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Full AdderCin A B S(um) Cout0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
00 01 11 10
0 0 1 0 1
1 1 0 1 0
Cin AB
BACin
B)(ACin)BACin(
)BABA(CinAB)BACin(
BACinCinABBACinBACinS
00 01 11 10
00 0 1 0
1 0 1 1 1
Cin AB
ABCinACinBCout
00 01 11 10
00 0 1 0
1 0 1 1 1
Cin AB
B)Cin(AAB)BABACin(ABCout
Or
Full Adder
A
B
Cin
Co
Sum
H.A. H.A.
Sum Cin A B
B)Cin(AABCout
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Full Adder
Co
Sum
Half Adder
Sum
Co
A
B
Half Adder
Sum
Co
A
BB
A
Cin
Sum Cin A B
B)Cin(AABCout
Circuit Diagram for the Full Adder A A
BB
RRSUMSUM
QQCARRYCARRY
CCININ
Sum Cin A B
ABCinACinBCout
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4-bit Ripple Adder using Full Adder
Full Adder
A B
CinCout
S
S0
A0 B0
Full Adder
A B
CinCout
S
S1
A1 B1
Full Adder
A B
CinCout
S
S2
A2 B2
Full Adder
A B
CinCout
S
S3
A3 B3
Carry
A
B
S
C
Half Adder
A
BCin
Cout
S
H.A. H.A.
Full Adder
Disain Subtractor
A – B = A + (-B) Lakukan komplemen 2 pada B
Jadikan penjumlahan A dan komplemen 2 dari B
Full Adder
A B
CinCout
S
S0
A0
Full Adder
A B
CinCout
S
S1
A1
Full Adder
A B
CinCout
S
S2
A2
Full Adder
A B
CinCout
S
S3
A3
B0B1B2B3
C
Subtract
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Sebuah rangkaian Subtractor terdiri dari Half Subtractordan Full Subtractor .
Half Subtractor mengurangkan dua buah bit input, dan
menghasilkan nilai hasil pengurangan (Remain) dan nilai yang dipinjam (Borrow-out).
Half Subtractor diletakkan sebagai pengurang dari bit-bitterendah (Least Significant Bit).
ADDER/SUBSTRACTOR UNIT
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