This document provides information about decimal and binary number systems including: 1) Tables that show decimal numbers and their equivalent binary representations from 0 to 15 and other examples up to 100. 2) Examples of converting between decimal and binary with steps shown for converting 1011, 100101, 13, 27, and 114 between the number systems. 3) Practice problems and solutions for adding, subtracting, and converting between decimal and binary.

1. Decimal vs Binary

2. Decimal Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
10 1010
Decimal Binary
11 1011
12 1100
13 1101
14 1110
15 1111
20 10100
25 11001
30 11110
40 101000
50 110010
100 1100100

3. Binary to Decimal
(1011)2 =(?)10

4. Binary to Decimal
(1011)2 =(11)10

5. Binary to Decimal
(100101)2 =(?)10

6. Binary to Decimal
(100101)2 =(37)10

7. Decimal to Binary
(13)10 = (?)2

8. Decimal to Binary
(13)10 = (1101)2

9. Decimal to Binary
(27)10 = (?)2

10. Decimal to Binary
(27)10 = (11011)2

11. Decimal to Binary
(114)10 = (?)2

12. Decimal to Binary
(114)10 = (1110010)2

13. Adding in binary
1011
+ 111
???

14. Adding in binary
1011
+ 111
10010

15. Adding in binary
10100111
+ 1000111
????????

16. Adding in binary
10100111
+ 1000111
11101110

17. Subtraction in binary
111101
- 100101
????

18. Subtraction in binary
111101
- 100101
11000

19. Subtraction in binary
1001
- 10
????

20. Subtraction in binary
1001
- 10
111

21. Subtraction in binary
11001010
- 10011011
???????

22. Subtraction in binary
11001010
- 10011011
101111

23. Subtraction in binary
11011010
- 10011111
?

24. Subtraction in binary
11011010
- 10011111
111011

25. Addition in binary
1101
+ 10111
?

26. Addition in binary
1101
+ 10111
100100