2. Select all and only the correct choices below.

Question

2. Select all and only the correct choices below.

(a) Suppose you were told that the positive integer n1 has the property that n1 div 2 = 0. Which

of the following can you conclude?

i. n1 has a binary (base 2) expansion

ii. n1 has a ternary (base 3) expansion

iii. n1 has a decimal (base 10) expansion

iv. n1 has a hexadecimal (base 16) expansion

v. n1 has a base 2 fixed-width 1 expansion

vi. n1 has a base 2 fixed-width 3 expansion

vii. n1 has a base 2 fixed-width 20 expansion

2. Select all and only the correct choices below.

(b) Suppose you were told that the positive integer n2 has the property that n2 mod 4 = 0. Which

of the following can you conclude?

i. the leftmost symbol in the binary (base 2) expansion of n2 is 1

ii. the leftmost symbol in the base 4 expansion of n2 is 1

iii. the leftmost symbol in the octal (base 8) expansion of n2 is 1

iv. the rightmost symbol in the binary (base 2) expansion of n2 is 0

v. the rightmost symbol in the base 4 expansion of n2 is 0

vi. the rightmost symbol in the octal (base 8) expansion of n2 is 0

Answer 1

In base b, the unit digit is the remainder mod b, so

2mod 3 = 2, so the units digit is 2.

This means that in the first problem, you know a) n1 in binary has a units digit of 0.

In the second problem, the right most digit (unit) Is zero.