Labs 1.1-1.4

Homework Labs 1.1 - 1.4 Thursday 8:30-12:30 6/25/2013
Exercise 1.1 Base 10
Mapping for decimal number 2931
10^3 10^2 10^1 10^0
2 9 3 1
2x1000=2000 + 9x100=900 + 3x10=30 + 1x1=1 = 2931

Exercise 1.1.2
Mapping for binary number 110 base 2
4 2 1
* * *
1 1 0
= = =
4 + 2 + 0= 6

Exercise 1.1.3
Mapping for binary number 11 base 2
2 1
* *
1 1
= =
2 + 1= 3

Exercise 1.1.4
Mapping for binary number 10010 base 2
16 8 4 2 1
* * * * *
1 0 0 1 0
= = = = =
16 + 0 + 0 + 2 + 0= 18

Exercise 1.1.5
Mapping for binary number 11100010 base 2
128 64 32 16 8 4 2 1
* * * * * * * *
1 1 1 0 0 0 1 0
= = = = = = = =
128 64 32 0 0 0 2 0= 226

Exercise 1.1.6
Binary conversion for decimal 156 base 10

156-128=28-16=12-8=4-4=0
128 64 32 16 8 4 2 1
1 0 0 1 1 1 0 0

Exercise 1.1.7
Binary conversion for decimal 255

255-128=127-64=63-32=31-16=15-8=7-4=3-2=1-1=0
128 64 32 16 8 4 2 1
1 1 1 1 1 1 1 `1

Exercise 1.1.8
Binary conversion for decimal 200

200-128=72-64=8-8=0
128 64 32 16 8 4 2 1
1 1 0 0 1 0 0 0

Lab 1.1 Reviews
1) Convert the decimal value 127 to binary.

127-64=63-32=31-16=15-8=7-4=3-2=1-1=0
64 32 16 8 4 2 1
1 1 1 1 1 1 1

2) Explain why values 10 base 2 and 0010 base 2 are equivalent- Two digits start over, and next digit to convert from a base 10 integer numeral to its base 2 equivalent.
3) When you multiply 2 by the power of you get 1,2,4,8,16,32 etc.
4) It wouldn’t be that difficult you just have to ally the correct formulas.

Exercise 1.2.1
Binary addition for 110 base 2 + 1001 base 2
1 0 0 1 + + +
1 1 0 = = =
1 1 1 1

Exercise 1.2.2
Adding binary 110 base 2 + 101 base 2

1 1 0
+ + +
1 0 1 = = =
1 1 1 1 One plus one means you carry the one its one zero not 10

Exercise 1.2.3
Adding binary 111 base 2 and 111 base 2

Carry 1 1
1 1 1
+ + +
1 1 1 = = =
1 1 1 0 one plus one