Question 21: Convert decimal 768 to binary.
Solution: 768 ÷ 2 = 384, remainder 0
384 ÷ 2 = 192, remainder 0
192 ÷ 2 = 96, remainder 0
96 ÷ 2 = 48, remainder 0
48 ÷ 2 = 24, remainder 0
24 ÷ 2 = 12, remainder 0
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: 1100000000. So, 768
in binary is 1100000000.
Question 22: Convert binary 101111001 to decimal.
Solution: 1 × 2^8 = 256
0 × 2^7 = 0
1 × 2^6 = 64
1 × 2^5 = 32
1 × 2^4 = 16
1 × 2^3 = 8
0 × 2^2 = 0
0 × 2^1 = 0
1 × 2^0 = 1
Add them up: 256 + 64 + 32 + 16 + 8 + 1 = 377. So, 101111001 in
decimal is 377.
Question 23: Convert decimal 430 to binary.
Solution: 430 ÷ 2 = 215, remainder 0
215 ÷ 2 = 107, remainder 1
107 ÷ 2 = 53, remainder 1
53 ÷ 2 = 26, remainder 1
26 ÷ 2 = 13, remainder 0
13 ÷ 2 = 6, remainder 1
6 ÷ 2 = 3, remainder 0
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 110101110. So, 430 in
binary is 110101110.
Question 24: Convert binary 111000011 to decimal.
Solution: 1 × 2^8 = 256
1 × 2^7 = 128
1 × 2^6 = 64
0 × 2^5 = 0
0 × 2^4 = 0
0 × 2^3 = 0
1 × 2^2 = 4
1 × 2^1 = 2
1 × 2^0 = 1
Add them up: 256 + 128 + 64 + 4 + 2 + 1 = 455. So, 111000011 in
decimal is 455.
Question 25: Convert decimal 235 to binary.
Solution: 235 ÷ 2 = 117, remainder 1
117 ÷ 2 = 58, remainder 1
58 ÷ 2 = 29, remainder 0
29 ÷ 2 = 14, remainder 1
14 ÷ 2 = 7, remainder 0
7 ÷ 2 = 3, remainder 1
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 11101011. So, 235 in
binary is 11101011.
Question 26: Convert binary 101010010 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
0 × 2^2 = 0
1 × 2^1 = 2
0 × 2^0 = 0
Add them up: 256 + 64 + 16 + 2 = 338. So, 101010010 in decimal is 338.
Question 27: Convert decimal 1024 to binary.
Solution: 1024 ÷ 2 = 512, remainder 0
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: 10000000000. So, 1024
in binary is 10000000000.
Question 28: Convert binary 110111001 to decimal.
Solution: 1 × 2^8 = 256
1 × 2^7 = 128
0 × 2^6 = 0
1 × 2^5 = 32
1 × 2^4 = 16
1 × 2^3 = 8
0 × 2^2 = 0
0 × 2^1 = 0
1 × 2^0 = 1
Add them up: 256 + 128 + 32 + 16 + 8 + 1 = 441. So, 110111001 in
decimal is 441.
Question 29: Convert decimal 875 to binary.
Solution: 875 ÷ 2 = 437, remainder 1
437 ÷ 2 = 218, remainder 1
218 ÷ 2 = 109, remainder 0
109 ÷ 2 = 54, remainder 1
54 ÷ 2 = 27, remainder
0 27 ÷ 2 = 13, remainder 1
13 ÷ 2 = 6, remainder 1
6 ÷ 2 = 3, remainder 0
3 ÷ 2 = 1, remainder 1
1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top gives: 1101101011. So, 875
in binary is 1101101011.
Question 30: Convert binary 1001110010 to decimal.
Solution: 1 × 2^9 = 512
0 × 2^8 = 0
0 × 2^7 = 0
1 × 2^6 = 64
1 × 2^5 = 32
1 × 2^4 = 16
0 × 2^3 = 0
0 × 2^2 = 0
1 × 2^1 = 2
0 × 2^0 = 0
Add them up: 512 + 64 + 32 + 16 + 2 = 626. So, 1001110010 in decimal
is 626.
Question 31: Convert decimal 300 to binary.
Solution: 300 ÷ 2 = 150, remainder 0
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: 100101100. So, 300 in
binary is 100101100.
Question 32: Convert binary 1110101101 to decimal.
Solution: 1 × 2^9 = 512
1 × 2^8 = 256
1 × 2^7 = 128
0 × 2^6 = 0
1 × 2^5 = 32
0 × 2^4 = 0
1 × 2^3 = 8
1 × 2^2 = 4
0 × 2^1 = 0
1 × 2^0 = 1
Add them up: 512 + 256 + 128 + 32 + 8 + 4 + 1 = 941. So, 1110101101 in
decimal is 941.