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Understanding Binary and Decimal Number Systems

Learn about Binary and Decimal numbers, their places and values, counting methods, and how to convert between them. Explore Nybbles, Bytes, and basic arithmetic in both systems.

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Understanding Binary and Decimal Number Systems

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  1. Binary Lesson 2Bytes

  2. Base Ten Normal Numbers Each place has one of these values: 0 1 2 3 4 5 6 7 8 9 147 = 1*100 + 4*10 + 7 Or 1*10^2 + 4*10^1 + 7*10^0

  3. Base Ten 147 Hundreds placeNumber of hundreds 10^2 Ones placeNumber of ones 10^0 Tens placeNumber of tens 10^1

  4. Base Two Binary Numbers Each place has one of these values: 0 1 11 = 1 * 2 + 1 = 3 Or 1*2^1 + 2^0

  5. Base Two 101 Fours placeNumber of fours 2^2 Ones placeNumber of ones 2^0 Twos placeNumber of twos 2^1

  6. Counting to 7 Base Two Base Ten 0 0 1 1 10 2 11 3 100 4 101 5 110 6 111 7

  7. Counting to 15 Base Two Base Ten Base Two Base Ten 0 0 1000 8 1 1 1001 9 10 2 1010 10 11 3 1011 11 100 4 1100 12 101 5 1101 13 110 6 1110 14 111 7 1111 15

  8. Four Bits Make a Nybble 4s 2s 1s 8s 1001

  9. Eight Bits Make a Byte 128s 64s 64s 32s 32s 32s 16s 16s 16s 8s 8s 8s 8s 4s 4s 4s 4s 2s 2s 2s 1s 1s 10011001 So this number is 128 + 16 + 8 + 1 = 153

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