Addizione 1
(1000)2 + (111)2 = ?
1000 + | 1000 + | 1000 + | 1000 + | 1000 +
111 = | 111 = | 111 = | 111 = | 111 =
------ | ------ | ------ | ------ | ------
| 1 | 11 | 111 | 1111
(1000)2 + (111)2 = (1111)2
In base 10
8 + 7= 15
In base 2
1000 + 111 = 1000 + 100+10+1= 1111
(1000)2 + (111)2 = 8+0+0+0 + 4+2+1= 8 + 4 + 2 + 1= (1111)2
Addizione 2
(1011)2 + (101)2 = ?
| 1 | 11 | 111 | 1111 | 1111
1011 + | 1011 + | 1011 + | 1011 + | 1011 + | 1011 +
101 = | 101 = | 101 = | 101 = | 101 = | 101 =
------ | ------ | ------ | ------ | ------- | -------
| 0 | 00 | 000 | 0000 | 10000
(1011)2 + (101)2 = (10000)2
In base 10
11 + 5= 10+1 + 5= 10 + 1+5= 10 + 6= 16
In base 2
1011 + 101 = 1000+10+1 + 100+1= 1000 + 100 + 10 + 1+1= 1000 + 100 + 10+10= 1000 + 100+100= 1000+1000= 10000
(1011)2 + (101)2 = 8+0+2+1 + 4+0+1= 8 + 4 + 2 + 1+1= 8 + 4 + 2+2= 8 + 4+4= 8+8= 16= (10000)2
Addizione 3
(1111)2 + (111)2 = ?
| 1 | 11 | 111 | 1111 | 1111
1111 + | 1111 + | 1111 + | 1111 + | 1111 + | 1111 +
111 = | 111 = | 111 = | 111 = | 111 = | 111 =
------ | ------ | ------ | ------ | ------- | -------
| 0 | 10 | 110 | 0110 | 10110
(1111)2 + (111)2 = (10110)2
In base 10
15 + 7= 10+5 + 7= 10 + 5+7= 10+10 + 2= 20 + 2= 22
In base 2
1111 + 111 = 1000+100+10+1 + 100+10+1= 1000 + 100+100 + 10+10 + 1+1= 1000 + 100+100 + 10+10+10= 1000 + 100+100+100 + 10= 1000+1000 + 100 + 10= 10000 + 100 + 10= 10110
(1111)2 + (111)2 = 8+4+2+1 + 4+2+1= 8 + 4+4 + 2+2 + 1+1= 8 + 4+4 + 2+2+2= 8 + 4+4+4 + 2= 8+8 + 4 + 2= 16 + 4 + 2= (10110)2
Sottrazione 1
(1111)2 - (111)2 = ?
1111 - | 1111 - | 1111 - | 1111 - | 1111 -
111 = | 111 = | 111 = | 111 = | 111 =
------ | ------ | ------ | ------ | ------
| 0 | 00 | 000 | 1000
(1111)2 - (111)2 = (1000)2
In base 10
15 - 7
= 8
(1111)2 - (111)2= 8+4+2+1 - (4+2+1)= 8+(4-4)+(2-2)+(1-1)= 8+0+0+0= (1000)2
Sottrazione 2
(1101)2 - (11)2 = ?
| | -1 +2 | -1 +2 | -1 +2
1101 - | 1101 - | 1 1 0 1 - | 1 1 0 1 - | 1 1 0 1 -
11 = | 11 = | 1 1 = | 1 1 = | 1 1 =
------ | ------ | ------------- | ------------- | -------------
| 0 | 1 0 | 0 1 0 | 1 0 1 0
(1101)2 - (11)2 = (1010)2
In base 10
13 - 3
= 10+3 - 3= 10 + 3-3= 10
(1101)2 - (11)2= 8+4+0+1 - (2+1)= 8+4+(0-2)+(1-1)= 8+4+(0-2)+0= 8+0+(2+2-2)+0= 8+0+2+0= (1010)2
Sottrazione 3
(1101)2 - (111)2 = ?
| | | -1 +2 | -1 +2
| | -1 +2 | -1 +2 | -1 +2
1101 - | 1101 - | 1 1 0 1 - | 1 1 0 1 - | 1 1 0 1 -
111 = | 111 = | 1 1 1 = | 1 1 1 = | 1 1 1 =
------ | ------ | ------------- | -------------- | --------------
| 0 | 1 0 | 1 1 0 | 0 1 1 0
(1101)2 - (111)2 = (110)2
In base 10
13 - 7= 6
(1101)2 - (111)2
= 8+4+0+1 - (4+2+1)
= 8+(4-4)+(0-2)+(1-1)
= 8+0+(0-2)+0
= 8+(0-4)+(2+2-2)+0
= 8+(0-4)+2+0
= (8-8)+(4+4-4)+2+0
= 0+4+2+0
= (110)2
Moltiplicazione 1
(110)2 * (101)2 = ?
110 * | 110 * | 110 * | 110 * | 110 *
101 = | 101 = | 101 = | 101 = | 101 =
----- | ----- | ------ | ------- | -------
| 110 | 110 | 110 | 110
| | 000. | 000. | 000.
| | | 110.. | 110..
| | | | -------
| | | | 11110
(110)2 * (101)2 = (11110)2
In base 10
6 * 5 = 30
In base 2
110 * 101= 110 * (100+0+1)= 110*100 + 110*0 + 110*1= 11000 + 0 + 110
…= 11110
(110)2 * (101)2= (4+2+0) * (4+0+1)= (4+2+0)*4 + (4+2+0)*0 + (4+2+0)*1= 16+8+0 + 0+0+0 + 4+2+0= 16+8+4+2+0= (11110)2
Moltiplicazione 2
(111)2 * (111)2 = ?
111 * | 111 * | 111 * | 111 * | 111 * ||
111 = | 111 = | 111 = | 111 = | 111 = || 11
----- | ----- | ------ | ------- | -------- || 1111
| 111 | 111 | 111 | 111 || 111 +
| | 111. | 111. | 111. || 1110 +
| | | 111.. | 111.. || 11100 =
| | | | -------- || --------
| | | | 110001 || 110001
(111)2 * (111)2 = (110001)2
In base 10
7 * 7 = 49
In base 2
111 * 111= 111 * (100+10+1)= 111*100 + 111*10 + 111*1= 11100 + 1110 + 111
…= 110001
(111)2 * (111)2= (4+2+1) * (4+2+1)= (4+2+1)*4 + (4+2+1)*2 + (4+2+1)*1= 16+8+4 + (8+4+2) + (4+2+1)= 16+(8+8)+(4+4+4)+(2+2)+1= 16+(8+8)+(4+4+4+4)+0+1= 16+(8+8+8+8)+0+0+1= (16+16+16)+0+0+0+1= 32+16+0+0+0+1= (110001)2
Divisione 1
(10000)2 : (100)2 = ?
10000 : 100 = 1 | 10000 : 100 = 10 | 10000 : 100 = 100
100 | 100 | 100
--- | ---- | -----
..0 | ..00 | ..000
(10000)2 : (100)2 = (100)2
In base 10
16 = 4*4 + 0
In base 2
10000
= 100 * 100
Divisione 2
(110000)2 : (101)2 = ?
110000 : 101 = 1 | 110000 : 101 = 10 || -1 +2
101 | 101 || 1 1 0 -
--- | ---- || 1 0 1 =
..1 | ..10 || ----------
| || . . 1
| ||
--------------------+-----------------------++----------------
| ||
110000 : 101 = 100 | 110000 : 101 = 1001 || -1 +2
101 | 101 || -1 +2
----- | ------ || -1 +2
..100 | ..1000 || 1 0 0 0 -
| 101 || 1 0 1 =
| ---- || --------------
| ..11 || . . 1 1
(110000)2 : (101)2 = (1001)2, resto=(11)2
In base 10
48 = 9*5 + 3
Controlla!
110000
= 1000 * 110
= 1000 * (101+1)
= 1000*101 + 1000
= 1000*101 + (101+11)
= 1000*101 + 1*101 + 11
= (1000+1) * 101 + 11
= 1001 * 101 + 11