Answer:
[tex]321_{10} = 101000001_{2}[/tex]
[tex]1023_{10} = 1111111111_2[/tex]
[tex]100632_{10} = 11000100100011000_{2}[/tex]
Step-by-step explanation:
Given
a) 321
b) 1023
c) 100632
Required
Convert to decimal
To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;
Solving (a)
321 / 2 = 160 R 1
160 / 2 = 80 R 0
80 / 2 = 40 R 0
40 / 2 = 20 R 0
20 / 2 = 10 R 0
10 / 2 = 5 R 0
5 / 2 = 2 R 1
2 / 2 = 1 R 0
1 / 2 = 0 R 1
Hence;
[tex]321_{10} = 101000001_{2}[/tex]
Solving (b)
1023 / 2 = 511 R 1
511 / 2 = 255 R 1
255 / 2 = 127 R 1
127 / 2 = 63 R 1
63 / 2 = 31 R 1
31 / 2 = 15 R 1
15 / 2 = 7 R 1
7 / 2 = 3 R 1
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]1023_{10} = 1111111111_2[/tex]
Solving (c)
100632 / 2 = 50316 R 0
50316 / 2 = 25158 R 0
25158 / 2 = 12579 R 0
12579 / 2 = 6289 R 1
6289 / 2 = 3144 R 1
3144 / 2 = 1572 R 0
1572 / 2 = 786 R 0
786 / 2 = 393 R 0
393 / 2 = 196 R 1
196 / 2 = 98 R 0
98 / 2 = 49 R 0
49 / 2 = 24 R 1
24 / 2 = 12 R 0
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]100632_{10} = 11000100100011000_{2}[/tex]
