Problem Statement
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Goal: Learner will be able to convert a decimal number to its binary equivalent using the binary conversion chart Problem/Scenario: Decimal number: Binary equivalent:
42 00101010
128
64
32
16
8
4
2
1
0
0
1
0
1
0
1
0
Place Value Binary
Solution: 1. Which power of two in the binary conversion chart is less than or equal to 42? 32 is less than 42. 2. Place a one in the 32 column, and a zero in the columns that are greater than 32. 128
64
32
0
0
1
16
8
4
2
1
Place Value Binary
3. Subtract 32 from 42: 42 -32 10 4. Which power of two in the binary conversion chart is less than or equal 10? 8 is less than 10 5. Place a one in the 8 column, and a zero in the unused column(s) between 32 and 8. 128
64
32
16
8
0
0
1
0
1
4
2
1
Place Value Binary
6. Subtract 8 from 10: 10 -8 2 7. Which power of two in the binary conversion chart is less than or equal 2? 2 is equal to 2 8. Place a one in the 2 column, a zero in the unused columns between 8 and 2, and a zero in any columns after 2.
128
64
32
16
8
4
2
1
0
0
1
0
1
0
1
0
9. 10. Write out the completed binary number: 00101010 11. 00101010 is the binary equivalent of the decimal 42.
Place Value Binary
42 00101010
128
64
32
16
8
4
2
1
0
0
1
0
1
0
1
0
Place Value Binary
Solution: 1. Which power of two in the binary conversion chart is less than or equal to 42? 32 is less than 42. 2. Place a one in the 32 column, and a zero in the columns that are greater than 32. 128
64
32
0
0
1
16
8
4
2
1
Place Value Binary
3. Subtract 32 from 42: 42 -32 10 4. Which power of two in the binary conversion chart is less than or equal 10? 8 is less than 10 5. Place a one in the 8 column, and a zero in the unused column(s) between 32 and 8. 128
64
32
16
8
0
0
1
0
1
4
2
1
Place Value Binary
6. Subtract 8 from 10: 10 -8 2 7. Which power of two in the binary conversion chart is less than or equal 2? 2 is equal to 2 8. Place a one in the 2 column, a zero in the unused columns between 8 and 2, and a zero in any columns after 2.
128
64
32
16
8
4
2
1
0
0
1
0
1
0
1
0
9. 10. Write out the completed binary number: 00101010 11. 00101010 is the binary equivalent of the decimal 42.
Place Value Binary
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