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* (The binary number 100000 is decimal number 32)

To represent the decimal number 100,000 in binary requires seventeen digits:

11 00001 10101 00000

The digits in a binary number are exponents of 2 rather than 10, so that for a seventeen-digit number in binary, the digit places represent

65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1

11000011010100000 = 65536 + 32768 + (0x16384) + (0x8192) + (0x5096) + (0x2048) + 1024 + 512 + (0x256) + 128 + (0x64) + 32 + (0x16) + (0x8) + (0x4) + (0x2) + (0x1) = 100000

Subtraction tree:

100000 - 65536 = 34464

34464 - 32768 = 1696

no 16384

no 8192

no 4096

no 2048

1696 - 1024 = 672

672 - 512 = 160

no 256

160 - 128 = 32

no 64

32 - 32 = 0

no 16

no 8

no 4

no 2

no 1

= 11000011010100000

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Q: What is the binary number of 100000?
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