Rev0hbh Lec4 ADDER

7/21/2019 Rev0hbh Lec4 ADDER

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22/09/20

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



22/09/20

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.



22/09/20

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



22/09/20

7

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.



22/09/20

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).



22/09/20

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


A A BB QQ RR

00 00 00 00

00 11 00 11

11 00 00 11

11 11 11 00



22/09/20

Circuit Diagram Q = (~A • B) + (A • ~B)

QQ

A A A A

BBBB

XOR SymbolThe symbol for the XOR Gate:

A A

BB

QQ

Q = AQ = A BB++++



22/09/20

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.


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



22/09/20

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



22/09/20

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



22/09/20

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



22/09/20

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



22/09/20

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



22/09/20

Rev0hbh Lec4 ADDER

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