(a) Which of the following is greater? 10(2) or 11(2)
(b) Write in ascending order: 1011(2), 110(2), 1000(2)
(c) Find the value of: (1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (0 × 20)
(d) Expand and write: (1) 10101(2) (2) 11110(2)
(a) Which of the following is greater? 10(2) or 11(2)
(b) Write in ascending order: 1011(2), 110(2), 1000(2)
(c) Find the value of: (1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (0 × 20)
(d) Expand and write: (1) 10101(2) (2) 11110(2)
(a) 10(2)
21
20
1
0
∴ 10(2) = 1 × 21 + 0 × 20 = 1 × 2 + 0 × 1 = 2 + 0 = 2
11(2)
21
20
1
1
∴11(2) = 1 × 21 + 1 × 20 = 1 × 2 + 1 ×1 = 2 + 1 = 3
∴ 11(2) > 10(2)
(b) 110(2)
22
21
20
1
1
0
∴110(2) =1 × 22 + 1 × 21 + 0 × 20 = 1× 4 + 1 × 2 + 0 ×1 = 4 + 2 + 1 = 7
1000(2)
23
22
21
20
1
0
0
0
1000(2) = 1 × 23+ 0 × 22 + 0 × 21 + 0 × 20 = 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 8 + 0 + 0 + 0 = 8
1011(2)
23
22
21
20
1
0
1
1
1011(2) =1 × 23+ 0 × 22 +1 × 21 + 1 × 20
= 1 × 8 + 0 × 4 + 1 × 2 + 1 ×1
= 8 + 0 + 2 + 1
= 11
Hence, the ascending order of the given numbers is 110(2), 1000(2), 1011(2).
(c) (1 × 24) + (0 × 23) + (1× 22) + (0 × 21) + (0 × 20)
= (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (0 × 1)
= 16 + 0 + 4 + 0 + 0
= 16 + 4 = 20
(d) (1) 10101(2)
24
23
22
21
20
1
0
1
0
1
∴ 10101(2) = 1 × 24 + 0 × 23+ 1 × 22 + 0 × 21 + 1 × 20
(2) 11110(2)
24
23
22
21
20
1
1
1
1
0
∴ 11110(2) = 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20
(a) 10(2)
|
21 |
20 |
|
1 |
0 |
∴ 10(2) = 1 × 21 + 0 × 20 = 1 × 2 + 0 × 1 = 2 + 0 = 2
11(2)
|
21 |
20 |
|
1 |
1 |
∴11(2) = 1 × 21 + 1 × 20 = 1 × 2 + 1 ×1 = 2 + 1 = 3
∴ 11(2) > 10(2)
(b) 110(2)
|
22 |
21 |
20 |
|
1 |
1 |
0 |
∴110(2) =1 × 22 + 1 × 21 + 0 × 20 = 1× 4 + 1 × 2 + 0 ×1 = 4 + 2 + 1 = 7
1000(2)
|
23 |
22 |
21 |
20 |
|
1 |
0 |
0 |
0 |
1000(2) = 1 × 23+ 0 × 22 + 0 × 21 + 0 × 20 = 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 8 + 0 + 0 + 0 = 8
1011(2)
|
23 |
22 |
21 |
20 |
|
1 |
0 |
1 |
1 |
1011(2) =1 × 23+ 0 × 22 +1 × 21 + 1 × 20
= 1 × 8 + 0 × 4 + 1 × 2 + 1 ×1
= 8 + 0 + 2 + 1
= 11
Hence, the ascending order of the given numbers is 110(2), 1000(2), 1011(2).
(c) (1 × 24) + (0 × 23) + (1× 22) + (0 × 21) + (0 × 20)
= (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (0 × 1)
= 16 + 0 + 4 + 0 + 0
= 16 + 4 = 20
(d) (1) 10101(2)
|
24 |
23 |
22 |
21 |
20 |
|
1 |
0 |
1 |
0 |
1 |
∴ 10101(2) = 1 × 24 + 0 × 23+ 1 × 22 + 0 × 21 + 1 × 20
(2) 11110(2)
|
24 |
23 |
22 |
21 |
20 |
|
1 |
1 |
1 |
1 |
0 |
∴ 11110(2) = 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20
