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The largest number with three digits in base two is 111, which equals seven.

Other answer:

largest 3 digit number = 999

base 2=binary

00000000000000000000000000=0

00000000000000000000000001=1

00000000000000000000000010=2

00000000000000000000000100=4

999/2=~500

log 500/log 2=8.9->9 ->9 zeroes after 1

2^9=512

1000000000=512

1100000000=512+256=768

1110000000=512+256+128=896

1111000000=512+256+128+64=960

1111100000=512+256+128+64+32=992

1111100111=512+256+128+64+32+4+2+1=999

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Q: What is the largest 3 digit number in base 2?
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