Number System
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This document discusses techniques for converting between different numeric bases, including binary, decimal, octal, and hexadecimal. It explains that conversion between bases involves representing numbers in one base using the digits of another base, through techniques like multiplying bits by place values, dividing and tracking remainders, and grouping/pairing digits. Examples are provided to demonstrate converting between bases like binary to decimal to octal to hexadecimal and vice versa.
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Number System
- 5. Base Weight 12510 =>5 × 100 2 × 101 1 × 102 5 20 100 = = = 125
- 7. Technique –Multiply each bit by 2n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results
- 8. 1010112 => 1 x 20 = 1 1 x 21 = 2 0 x 22 = 0 1 x 23 = 8 0 x 24 = 0 1 x 25 = 32 4310
- 10. Technique –Multiply each bit by 8n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results
- 11. 7248 => 4 x 80 = 4 2 x 81 = 16 7 x 82 = 448 46810
- 13. Technique –Multiply each bit by 16n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results
- 14. ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560 274810
- 16. Technique –Divide by two, keep track of the remainder –First remainder is bit 0 –Second remainder is bit 1
- 17. 12510 = ?2 12510 = 11111012 2 125 2 62 1 2 31 0 2 15 1 2 7 1 2 3 1 1 1
- 19. Technique Convert each octal digit to a equivalent binary representation
- 20. 7058 = ?2 7 0 5 111 000 101 7058 = 1110001012
- 22. Technique Convert each hexadecimal digit to a 4-bit equivalent binary representation
- 23. 10AF16 = ?2 1 0 A F 0001 0000 1010 1111 10AF16 = 00010000101011112
- 25. Technique –Divide by 8 –Keep track of the remainder
- 26. 123410 = ?8 123410 = 23228 8 1234 2 8 154 2 8 19 3 2 2
- 28. Technique –Divide by 16 –Keep track of the remainder
- 29. 123410 = ?16 123410 = 4D216 16 123 4 16 77 2 16 4 13=D 0 4
- 31. Technique –Group bits in threes, starting on right –Convert to octal digits
- 32. 10110101112 = ?8 001 011 010 111 1 3 2 7 10110101112 = 13278 From right to left pairing of 3 binary digits
- 34. Technique Group bits in fours, starting on right Convert to hexadecimal digits
- 35. 10101110112 = ?16 0010 1011 1011 2 B B 10101110112 = 2BB16 From right to left pairing of 4 binary digits
- 37. Octal to Hexadecimal Technique Use binary as an intermediary
- 38. 4568 = 1001011102 4 5 6 0001 0010 1110 1 2 E 10768 = 12E16 From right to left pairing of 4 binary digits
- 40. Technique Use binary as an intermediary
- 41. Example 1F0C16 = 11111000011002 1 F 0 C 001 111 100 001 100 1 7 4 1 4 1F0C16 = 174148 From right to left pairing of 3 binary digits
- 42. Thank You