Dinyatakan dengan sign, bilangan magnitude dan posisi titik radiks. Titik radiks memisahkan bilangan bulat dan pecahan. Penggunaan titik radiks berkaitan dengan jajaran bilangan yang dapat ditampung oleh komputer.
Representasi Fixed-point : titik radiks selalu pada posisi tetap.
Representasi Floating-point :
a = m x r e
r = radiks, m = mantissa, e = eksponen
Untuk menyatakan bilangan yang sangat besar atau sangat kecil, dengan menggeser titik radiks dan mengubah eksponen untuk mempertahankan nilainya.
5,67 137,12
43,09 + 10,09 –
48,76 127,03
PENJUMLAHAN dan PENGURANGAN dalam Basis X
(67)8 (1101)2 (A19)16
(35)8 + (1001)2 + ( 53)16 –
(124)8 (10110)2 (9C6)16
ARITMATIKA FLOATING POINT
Penambahan dan Pengurangan
0,63524 x 103
0,63215 x 103 +
1,26739 x 103 0,126739 x 104
0,11000 x 22 0,11000 x 23
0,10100 x 23 0,01010 x 23 –
0,01110 x 23
Perkalian
(0,253 x 102) x (0,124 x 103)
= (0,253) x (0,124) x 102+3
= 0,031 x 105 0,31 x 104
Representasi Bilangan Positif dan Negatif pada bilangan BINER
1. Label tanda konvensional : + dan –
Contoh : +4 dan -4
2. Menggunakan posisi digit sebelah kiri (MSB) sebagai
sign digit (0 untuk positif dan 1 untuk negatif).
Contoh : Sign-Magnitude +9 dalam 8 bit = 00001001
Sign-Magnitude -4 dalam 4 bit = 1100
Magnitude dari bilangan positif dan negatif sama hanya berbeda pada sign digitnya/MSB.
3. Representasi Komplemen-1
Angka nol diubah menjadi satu dan satu menjadi nol.
Contoh : Dalam 8 bit
+12 = 00001100
-12 = 11110011
4. Representasi Komplemen-2
Dengan representasi komplemen-1 ditambah 1. Contoh : Dalam 8 bit
-12 = 11111011 (Komplemen-1)
1 +
= 11111100 (Komplemen-2)
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