A binary string is a word containing only Os and 1s. In a binary string, a 1-run is a non-extendable substring containing only 1s. Given a positive integer n, let B(n) be the number of 1-runs in the binary representation of n. For example, B(107) = 3 since 107 in binary is 1101011 which has exactly three 1-runs. What is the following expression equal to? B(1) + B(2) + B(3) + ... + B(255)

Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a is an integer.is is also an integer. Since 10n+4 equals 2 times an integer, 10n+ 4 is even.

Determine whether each integer has multiplicative inverse modulo 1001. If it does, find the inverse. (a) a = 156 (b) b = 323

Let x be an integer. Prove or provide a counterexample: If 4x+7 is odd, then x is odd.