Question 1
Convert the following binary numbers to decimal:
- 1001
- 1101101
- 1000001
- 1111111
- 100000011000001
- 101010101010101
- 110101
- 10101100
- 11111010001
Check your answers (you can google search “1001 binary to decimal” or similar to get an answer)
| 1001 |
2³ + 2⁰ |
9 |
| 1101101 |
2⁶ + 2⁵ + 2³ + 2² + 2⁰ |
109 |
| 1000001 |
2⁶ + 2⁰ |
65 |
| 1111111 |
2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2¹ + 2⁰ |
127 |
| 100000011000001 |
2¹⁴ + 2⁷ + 2⁶ + 2⁰ |
16577 |
| 101010101010101 |
2¹⁴ + 2¹² + 2¹⁰ + 2⁸ + 2⁶ + 2⁴ + 2² + 2⁰ |
21845 |
| 110101 |
2⁵ + 2⁴ + 2² + 2⁰ |
53 |
| 10101100 |
2⁷ + 2⁵ + 2³ + 2² |
172 |
| 11111010001 |
2¹⁰ + 2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2⁰ |
2001 |
Question 2
Convert the following decimal numbers in binary: - 33 - 58 - 263 - 3450 - 9349 - 724
| 33 |
32 + 1 = 2⁵ + 2⁰ |
100001 |
| 58 |
32 + 16 + 8 + 2 = 2⁵ + 2⁴ + 2³ + 2¹ |
111010 |
| 263 |
256 + 4 + 2 + 1 = 2⁸ + 2² + 2¹ + 2⁰ |
100000111 |
| 3450 |
2048 + 1024 + 256 + 64 + 32 + 16 + 8 + 2 = 2¹¹+2¹⁰+2⁸+2⁶+2⁵+2⁴+2³+2¹ |
110101111010 |
| 9349 |
8192 + 1024 + 128 + 4 + 1 = 2¹³ + 2¹⁰ + 2⁷ + 2² + 2⁰ |
1001001000101 |
| 724 |
512 + 128 + 64 + 16 + 4 = 2⁹ + 2⁷ + 2⁶ + 2⁴ + 2² |
1011010100 |
(263)10 = …
| 131 |
1 |
| 65 |
1 |
| 32 |
1 |
| 16 |
0 |
| 8 |
0 |
| 4 |
0 |
| 2 |
0 |
| 1 |
0 |
| 0 |
1 |
(3450)10 = …
| 1725 |
0 |
| 862 |
1 |
| 431 |
0 |
| 215 |
1 |
| 107 |
1 |
| 53 |
1 |
| 26 |
1 |
| 13 |
0 |
| 6 |
1 |
| 3 |
0 |
| 1 |
1 |
| 0 |
1 |
Reading from bottom to top: 1101 0111 1010
(9349)10 = …
| 4674 |
1 |
| 2337 |
0 |
| 1168 |
1 |
| 584 |
0 |
| 292 |
0 |
| 146 |
0 |
| 73 |
0 |
| 36 |
1 |
| 18 |
0 |
| 9 |
0 |
| 4 |
1 |
| 2 |
0 |
| 1 |
0 |
| 0 |
1 |
Reading from bottom to top: 10 0100 1000 0101
Question 3
Consider a 32-bit CPU: a. How many numbers can be represented on this CPU? b. What’s the largest unsigned number (positive numbers only)? c. What’s the largest signed number?
- 4,294,967,296 (232)
- 4,294,967,295
- 2,147,483,648 (231) Note that for signed numbers, one bit is reserved for the sign (+/-).
Question 4
What’s the smallest number which requires 12 bits?
212 = 4096 Note: Any number smaller than 4096, doesn’t require 12 bits to be represented in binary. 4096 is the smallest number which requires 12 bits.
Question 5
What’s the minimum numbers of bits required to store the value 16587.
- Represent the number in binary: 100 0000 1100 1011
- Count the number of bits required to represent this number.
The answer is 15 bits.
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