Changing a Decimal Number to an Octal Number Repeatedly divide by eight and record the remainder for each division – read “answer” upwards Example:
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Decimal Numbering System Ten symbols: 0, 1, 2, 3, 4, 5, 6, Example: 7061 in decimal (base 10) • 7061 10 Hexadecimal Number System Hexadecimal is
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0 101112 = 0 101 110 = 0 568 0 101112 = 0 1011 1000 = 0 B816 Problems Convert the following Binary Octal Decimal Hex 10011010 2705 2705 3BC
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Changing a Decimal Number to an Octal Number Repeatedly divide by eight and record the remainder for each division – read “answer” upwards Example:
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Octal and Hexadecimal Number Systems
OCTAL or BASE-8 numbers uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7 (count them!) and position plays
a major role in expressing their meaning. For example 53,7028 means5 x 84 + 3 x 83 + 7 x 82 + 0 x 81 + 2 x 80
4096's 512's Sixty-fours Eights Ones (Units)
To change this number to base 10, multiply each placeholder by the amount its location represents and
add: (5 x 4096) + (3 x 512) + (7 x 64) + (0 x 8) + (2 x 1) = 20,480 + 1536 + 448 + 0 + 1 = 22,46610 HEXADECIMAL or BASE-16 numbers uses sixteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, and E (count them!) and position plays a major role in expressing their meaning. For example 537CA16 means5 x 164 + 3 x 163 + 7 x 162 + C x 161 + A x 160
65,536's 4096's 256's Sidžteens Ones (Units)
To change this number to base 10, multiply each placeholder by the amount its location represents and
add: (5 x 65,536) + (3 x 4096) + (7 x 256) + (12 x 8) + (10 x 1) = 327,680 + 12,288 + 1792 + 96 + 10 =