Question

In our very first module, we looked at numeration systems and the different bases that various cultures used. The Babylonian system was base 60; the Mayan system was base 20 (almost); and our Hindu-Arabic system is base 10. You read in the Grace Hopper biography that computers use a base 2 system. In base 2, only two symbols are used, so all numbers are represented with 0s and 1s.

A. Change the number 100 (base ten) to a numeral in base two.
B. Change the number 1010101 (base two) to a numeral in base ten.
C. This is a fun problem! The moon is approximately 238,900miles from Earth.
Admiral Hopper explained to David Letterman that a nano-second is one-billionth of a second. The maximum distance that electricity (or light) can travel in one nano-second is approximately one foot. How many seconds will it take to send an electronic signal from Earth to the Moon? If the signal bounces right back, how long will it take for the signal to go to the moon and come back to Earth? In this episode, Leonard and the other guys send laser signal to the moon and back. Leonard will tell you how long it took for the signal to go to the moon and back.

Answer 1

1100100 base 2

85 base 10

2.522784 seconds

Explanation:

Convert 100 from base 10 to the base 2

Reduce 100 by 2 until 0 ; the reminder obtained is written from bottom to top.

2 | 100

2 | 50 r 0

2 | 25 r 0

2 | 12 r 1

2 | 6 r 0

2 | 3 r 0

2 | 1 r 1

__0 r 1

Arranging from the bottom : 1100100 base 2

100 base 10 = 1100100 base 2

1010101 base 2 to base 10

1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 1*2^2 + 0*2^1 + 1*2^0

64 + 0 + 16 + 0 + 4 + 0 + 1 = 85 base 10

C)

1 mile = 5280 feets

Distance from earth to moon = 238900 miles

Distance in feets :

(5280 * 238900) = 1261392000 feets

Total distance from moon and back to earth = 2 * 1261392000 = 2522784000 feets

Using the relation :

Speed = distance / time

Speed = 1 feet per nano second

Distance = 2522784000 feets

1 = 2522784000 / time

Time = 2522784000 nano seconds

Converting to second :

2522784000 / 1000000000

= 2.522784 seconds