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number theory intermediate

Problem

If

N

, written in base

2

, is

11000

, the integer immediately preceding

N

, written in base

2

, is:

(A)

10001

(B)

10010

(C)

10011

(D)

10110

(E)

10111

Solution

1100 0_{2} - 1_{2} = 1011 1_{2}

.

10111

Final answer

E