Activity 2.1.2
Conclusion
1. The decimal number system has served humans well since the beginning of mankind. Ug the caveman didn’t call it the decimal number system, but he undoubtedly used his fingers to count objects in his world. If the decimal system is so good, why do computer and other digital electronic devices use the binary number system?
Computers can only recognizes two states: on and off. Binary only has two numbers 1 and 0.
d
· 011010 (2)
4. How were you able to determine this?
because the one is further to the left, so it will probably be a bigger number
Decimal
Number
Binary Number
MSB
LSB
0 =
0
0
0
0
1 =
0
0
0
1
2 =
0
0
1
0
3 =
0
0
1
1
4 =
0
1
0
0
5 =
0
1
0
1
6 =
0
1
1
0
7 =
0
1
1
1
8 =
0
0
1
0
9 =
1
0
0
1
10 =
1
0
1
0
11 =
1
0
1
1
12 =
0
0
1
1
13 =
1
1
0
1
14 =
1
1
1
0
15 =
1
1
1
1
1. The decimal number system has served humans well since the beginning of mankind. Ug the caveman didn’t call it the decimal number system, but he undoubtedly used his fingers to count objects in his world. If the decimal system is so good, why do computer and other digital electronic devices use the binary number system?
Computers can only recognizes two states: on and off. Binary only has two numbers 1 and 0.
- Now that we are using a number system other the decimal, it is important to properly subscript our numbers (i.e., 3510, 23410, 100102, etc.). Why is this so important? Provide at least three examples where neglecting to subscript numbers could lead to confusion.'
d
- Without performing the binary-to-decimal conversions, which of the following two binary numbers is the larger number :
· 011010 (2)
4. How were you able to determine this?
because the one is further to the left, so it will probably be a bigger number
- Perform the binary-to-decimal conversions and check your answer. Were you correct? yes
- Examine the table that you completed in the procedure portion of the activity. What do you notice about the LSB (least-significant-bit)? What do you notice about the middle bit? What do you notice about the MSB (most-significant-bit)? Do you observe a pattern here?
Decimal
Number
Binary Number
MSB
LSB
0 =
0
0
0
0
1 =
0
0
0
1
2 =
0
0
1
0
3 =
0
0
1
1
4 =
0
1
0
0
5 =
0
1
0
1
6 =
0
1
1
0
7 =
0
1
1
1
8 =
0
0
1
0
9 =
1
0
0
1
10 =
1
0
1
0
11 =
1
0
1
1
12 =
0
0
1
1
13 =
1
1
0
1
14 =
1
1
1
0
15 =
1
1
1
1