The document discusses converting decimal numbers to binary and hexadecimal numbers. It provides examples of converting the decimal numbers 20, 26, and 39 to their binary equivalents. It also addresses that the largest number that can be represented with 6 bits is 63, which is equal to 26 - 1 and results from having all 1s in the 6 bit positions, each worth powers of 2.

1. 1.9
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Converting from
Decimal to Binary and
Hexadecimal
MATH1003

2. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Goal
To be able to correctly convert a decimal number
into a binary number and a hexadecimal number.
MATH1003

3. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
MATH1003

4. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
MATH1003

5. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
Which bits need to be turned on?
MATH1003

6. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
Which bits need to be turned on?
MATH1003

7. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
Which bits need to be turned on?
MATH1003

8. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
Which bits need to be turned on?
MATH1003

9. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
Which bits need to be turned on?
MATH1003

10. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 20 to a binary number.
Digit
0 1 0 1 0 0
(Face value)
32 16 8 4 2 1
Place value
25 24 23 22 21 20
20 = 0101002
MATH1003

11. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

12. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

13. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

14. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

15. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

16. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 26 to a binary number.
Digit
0 1 1 0 1 0
(Face value)
Place value 32 16 8 4 2 1
26 = 0110102
MATH1003

17. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

18. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

19. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

20. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

21. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

22. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

23. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
39 = 1001112
MATH1003

24. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
MATH1003

25. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
MATH1003

26. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
1111112 = 63
MATH1003

27. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
1111112 = 63
= 64 - 1
MATH1003

28. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
1111112 = 63
= 64 - 1
= 26 - 1
MATH1003

29. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 6 bits?
Digit
1 1 1 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Note that the
exponent is equal to the
1111112 = 63 number of bits
= 64 - 1
= 26 - 1
MATH1003

30. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 8 bits?
Digit
1 1 1 1 1 1 1 1
(Face value)
Place value 128 64 32 16 8 4 2 1
MATH1003

31. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 8 bits?
Digit
1 1 1 1 1 1 1 1
(Face value)
Place value 128 64 32 16 8 4 2 1
111111112 = 255
MATH1003

32. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 8 bits?
Digit
1 1 1 1 1 1 1 1
(Face value)
Place value 128 64 32 16 8 4 2 1
111111112 = 255
= 256 - 1
MATH1003

33. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 8 bits?
Digit
1 1 1 1 1 1 1 1
(Face value)
Place value 128 64 32 16 8 4 2 1
111111112 = 255
= 256 - 1
= 28 - 1
MATH1003

34. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 12 bits?
MATH1003

35. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 12 bits?
1111111111112 = 212 - 1
MATH1003

36. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Numbers
What’s the biggest number that can be
represented by 12 bits?
1111111111112 = 212 - 1
= 4095
MATH1003

37. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

38. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

39. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

40. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

41. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

42. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
Which bits need to be turned on?
MATH1003

43. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
MATH1003

44. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Convert 39 to a binary number.
Digit
1 0 0 1 1 1
(Face value)
Place value 32 16 8 4 2 1
39 = 1001112
MATH1003

45. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
MATH1003

46. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number.
MATH1003

47. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
MATH1003

48. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
MATH1003

49. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
MATH1003

50. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
MATH1003

51. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
MATH1003

52. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
MATH1003

53. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem We stop
1
dividing once the
4 ÷ 2 = 2 rem 0
quotient is 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
MATH1003

54. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
MATH1003

55. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1 We write
9 ÷ 2 = 4 rem 1 down the
remainders
4 ÷ 2 = 2 rem 0 starting with
2 ÷ 2 = 1 rem 0 the last one
1 ÷ 2 = 0 rem 1
MATH1003

56. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1 We write
9 ÷ 2 = 4 rem 1 down the
remainders
4 ÷ 2 = 2 rem 0 starting with
2 ÷ 2 = 1 rem 0 the last one
1 ÷ 2 = 0 rem 1
39 =
MATH1003

57. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 =
MATH1003

58. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 1
MATH1003

59. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 1
MATH1003

60. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 10
MATH1003

61. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 10
MATH1003

62. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 100
MATH1003

63. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 100
MATH1003

64. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 1001
MATH1003

65. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 1001
MATH1003

66. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 10011
MATH1003

67. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 10011
MATH1003

68. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 100111
MATH1003

69. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 100111
MATH1003

70. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Let’s look at another method for converting decimal
numbers to binary.
Convert 39 to a binary number. 39 ÷ 2 = 19 rem 1
19 ÷ 2 = 9 rem 1
9 ÷ 2 = 4 rem 1
4 ÷ 2 = 2 rem 0
2 ÷ 2 = 1 rem 0
1 ÷ 2 = 0 rem 1
39 = 1001112
MATH1003

71. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number.
MATH1003

72. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
MATH1003

73. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
MATH1003

74. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
MATH1003

75. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
MATH1003

76. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
MATH1003

77. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
MATH1003

78. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
MATH1003

79. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
MATH1003

80. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
quotient
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
MATH1003

81. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
quotient remainder
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
MATH1003

82. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
quotient remainder
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
MATH1003

83. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
Here’s another example:
quotient remainder
Convert 105 to a binary number. 105 ÷ 2 = 52 rem 1
52 ÷ 2 = 26 rem 0
26 ÷ 2 = 13 rem 0
13 ÷ 2 = 6 rem 1
6 ÷ 2 = 3 rem 0
3 ÷ 2 = 1 rem 1
1 ÷ 2 = 0 rem 1
105 = 11010012
MATH1003

84. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
MATH1003

85. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Convert 125 to a hexadecimal number.
MATH1003

86. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Instead of dividing
Convert 125 to a hexadecimal number.
by 2, we divide by
16. Remember
that hexadecimal
is “base 16”.
MATH1003

87. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Convert 125 to a hexadecimal number.
MATH1003

88. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13
MATH1003

89. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13
7 ÷ 16 = 0 rem 7
MATH1003

90. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
hexadecimal?
Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13
7 ÷ 16 = 0 rem 7
MATH1003

91. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
Note that
hexadecimal? 13 = D
Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13
7 ÷ 16 = 0 rem 7
MATH1003

92. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
How can we modify the method we just looked at so
that it will work for converting decimal numbers to
Note that
hexadecimal? 13 = D
Convert 125 to a hexadecimal number. 125 ÷ 16 = 7 rem 13
7 ÷ 16 = 0 rem 7
125 = 7D16
MATH1003

93. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
MATH1003

94. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number.
MATH1003

95. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5
MATH1003

96. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5
248 ÷ 16 = 15 rem 8
MATH1003

97. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5
248 ÷ 16 = 15 rem 8
15 ÷ 16 = 0 rem 15
MATH1003

98. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5
248 ÷ 16 = 15 rem 8
15 ÷ 16 = 0 rem 15
MATH1003

99. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5 Note that
15 = F
248 ÷ 16 = 15 rem 8
15 ÷ 16 = 0 rem 15
MATH1003

100. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Hexadecimal
Here’s another example:
Convert 3973 to a hexadecimal number. 3973 ÷ 16 = 248 rem 5 Note that
15 = F
248 ÷ 16 = 15 rem 8
15 ÷ 16 = 0 rem 15
3973 = F8516
MATH1003

101. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
MATH1003

102. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
MATH1003

103. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number.
MATH1003

104. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
MATH1003

105. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a we
This time fractional
multiply instead of
part into binary? dividing
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
MATH1003

106. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
MATH1003

107. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
We use only
part into binary? the fractional part
in the next line
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
MATH1003

108. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
MATH1003

109. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
MATH1003

110. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
MATH1003

111. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
0.4 • 2 = 0.8
MATH1003

112. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
0.4 • 2 = 0.8
MATH1003

113. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary The “fractional part” is
the part to the right of
the point (or period).
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4 Notice here that
0.8 has appeared
0.4 • 2 = 0.8
again. Once that
happens, we know
that we have a
repeating pattern.
MATH1003

114. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4 Notice here that
0.8 has appeared
0.4 • 2 = 0.8
again. Once that
0.8 • 2 = 1.6 happens, we know
0.6 • 2 = 1.2 that we have a
0.2 • 2 = 0.4 repeating pattern.
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
MATH1003 0.2 • 2 = 0.4

115. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4 Notice here that
0.8 has appeared
0.4 • 2 = 0.8
again. Once that
0.8 • 2 = 1.6 happens, we know
0.6 • 2 = 1.2 that we have a
0.2 • 2 = 0.4 repeating pattern.
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
MATH1003 0.2 • 2 = 0.4

116. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4 Notice here that
0.8 has appeared
0.4 • 2 = 0.8
again. Once that
0.8 • 2 = 1.6 happens, we know
0.6 • 2 = 1.2 that we have a
0.2 • 2 = 0.4 repeating pattern.
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
MATH1003 0.2 • 2 = 0.4

117. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4 Notice here that
0.8 has appeared
0.4 • 2 = 0.8
again. Once that
0.8 • 2 = 1.6 happens, we know
0.6 • 2 = 1.2 that we have a
0.2 • 2 = 0.4 repeating pattern.
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
MATH1003 0.2 • 2 = 0.4

118. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
MATH1003

119. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
MATH1003

120. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
This time,
instead of reading
the 0s and 1s
upwards, we read
them downwards
MATH1003

121. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
0.7 = .1
MATH1003

122. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
0.7 = .1
MATH1003

123. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Decimal to Binary
How do we convert decimal numbers with a fractional
part into binary?
Convert 0.7 to a binary number. 0.7 • 2 = 1.4
0.4 • 2 = 0.8
0.8 • 2 = 1.6
0.6 • 2 = 1.2
0.2 • 2 = 0.4
0.7 = .10
MATH1003