Question 11: Convert decimal 25 to binary.
Solution: To convert 25 to binary, divide by 2 and record the
remainder. 25 ÷ 2 = 12, remainder 1
12 ÷ 2 = 6, remainder 0
6 ÷ 2 = 3, remainder 0
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 11001. So, 25 in
binary is 11001.
Question 12: Convert binary 10110 to decimal.
Solution: Starting from the rightmost digit, multiply each binary digit by 2 raised to the power of its position: 1 × 2^4 = 16 0 × 2^3 = 0 1 × 2^2 = 4 1 × 2^1 = 2 0 × 2^0 = 0 Add them up: 16 + 4 + 2 = 22. So, 10110 in decimal is 22.
Question 13: Convert decimal 150 to binary.
Solution: 150 ÷ 2 = 75, remainder 0
75 ÷ 2 = 37, remainder 1
37 ÷ 2 = 18, remainder 1
18 ÷ 2 = 9, remainder 0
9 ÷ 2 = 4, remainder 1
4 ÷ 2 = 2, remainder 0
2 ÷ 2 = 1, remainder 0
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 10010110. So, 150 in
binary is 10010110.
Question 14: Convert binary 10001011 to decimal.
Solution: 1 × 2^7 = 128
0 × 2^6 = 0
0 × 2^5 = 0
0 × 2^4 = 0
1 × 2^3 = 8
0 × 2^2 = 0
1 × 2^1 = 2
1 × 2^0 = 1
Add them up: 128 + 8 + 2 + 1 = 139. So, 10001011 in decimal is 139.
Question 15: Convert decimal 45 to binary.
Solution: 45 ÷ 2 = 22, remainder 1
22 ÷ 2 = 11, remainder 0
11 ÷ 2 = 5, remainder 1
5 ÷ 2 = 2, remainder 1
2 ÷ 2 = 1, remainder 0
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 101101. So, 45 in
binary is 101101.
Question 16: Convert binary 110100 to decimal.
Solution: 1 × 2^5 = 32
1 × 2^4 = 16
0 × 2^3 = 0
1 × 2^2 = 4
0 × 2^1 = 0
0 × 2^0 = 0
Add them up: 32 + 16 + 4 = 52. So, 110100 in decimal is 52.
Question 17: Convert decimal 512 to binary.
Solution: 512 ÷ 2 = 256, remainder 0
256 ÷ 2 = 128, remainder 0
128 ÷ 2 = 64, remainder 0
64 ÷ 2 = 32, remainder 0
32 ÷ 2 = 16, remainder 0
16 ÷ 2 = 8, remainder 0
8 ÷ 2 = 4, remainder 0
4 ÷ 2 = 2, remainder 0
2 ÷ 2 = 1, remainder 0
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 1000000000. So, 512
in binary is 1000000000.
Question 18: Convert binary 101010101 to decimal.
Solution: 1 × 2^8 = 256
0 × 2^7 = 0
1 × 2^6 = 64
0 × 2^5 = 0
1 × 2^4 = 16
0 × 2^3 = 0
1 × 2^2 = 4
0 × 2^1 = 0
1 × 2^0 = 1
Add them up: 256 + 64 + 16 + 4 + 1 = 341. So, 101010101 in decimal is
341.
Question 19: Convert decimal 202 to binary.
Solution: 202 ÷ 2 = 101, remainder 0
101 ÷ 2 = 50, remainder 1
50 ÷ 2 = 25, remainder 0
25 ÷ 2 = 12, remainder 1
12 ÷ 2 = 6, remainder 0
6 ÷ 2 = 3, remainder 0
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 11001010. So, 202 in
binary is 11001010.
Question 20: Convert binary 1101011 to decimal.
Solution: 1 × 2^6 = 64
1 × 2^5 = 32
0 × 2^4 = 0
1 × 2^3 = 8
0 × 2^2 = 0
1 × 2^1 = 2
1 × 2^0 = 1
Add them up: 64 + 32 + 8 + 2 + 1 = 107. So, 1101011 in decimal is 107.