4.10. Exercises
-
What are the decimal and hexadecimal representations for the value 0b01001010?
-
What are the binary and hexadecimal representations for the value 389?
-
As a five-armed creature, Sally the starfish prefers to represent numbers using a base 5 number system. If Sally gives you the base 5 number 1423, what is the equivalent decimal value?
-
Early Access Interactive Number Conversion Questions
Solutions
If your browser supports hidden solutions, click here to reveal them.
-
0b01001010 in decimal is:
In hexadecimal, it’s:
0100 1010 4 A -> 0x4A
-
Converting 389 to decimal…
Using powers of two:
-
256 fits into 389, so d8 should be a 1. That leaves 389 - 256 = 133.
-
128 fits into 133, so d7 should be a 1. That leaves 133 - 128 = 5.
-
64 does not fit into 5, so d6 should be a 0.
-
32 does not fit into 5, so d5 should be a 0.
-
16 does not fit into 5, so d4 should be a 0.
-
8 does not fit into 5, so d3 should be a 0.
-
4 fits into 5, so d2 should be a 1. That leaves 6 - 5 = 1.
-
2 fits does not fit into 1, so d1 should be a 0.
-
1 fits into 1, so d0 should be a 1. That leaves 1 - 1 = 0.
Thus, decimal 389 corresponds to 0b110000101.
Using repeated division:
-
389 is odd, so d0 should be a 1.
-
389 / 2 = 194, which is even, so d1 should be a 0.
-
194 / 2 = 97, which is odd, so d2 should be a 1.
-
97 / 2 = 48, which is even, so d3 should be a 0.
-
48 / 2 = 24, which is even, so d4 should be a 0.
-
24 / 2 = 12, which is even, so d5 should be a 0.
-
12 / 2 = 6, which is even, so d6 should be a 0.
-
6 / 2 = 3, which is odd, so d7 should be a 1.
-
3 / 2 = 1, which is odd, so d8 should be a 1.
-
1 / 2 = 0, so any digit numbered nine or above will be 0.
Thus, decimal 389 corresponds to 0b110000101.
Converting to hexadecimal:
0001 1000 0101 1 8 5 -> 0x185
-
-
1423 in base 5 converted to decimal is: