Lab 1.1
1.1.1
10⁰
10⁰
10¹
10¹
10²
10²
10³

10³

1

1

10

10

100

100

1000

1000

2931

2931

30
30
1
1
2000

2000

900
900
2
2
1
1
3
3
9
9
X X X X

1.1.2

2² 2¹ 2º

4 2 1
1
1
X X X
0
0
1
1

5
5
4
4
0
0
1
1

1.1.3
2² 2¹ 2º

4 2 1
0
0
X X X
1
1
1
1

3
3
0
0
2
2
1
1

1.1.4

24 2³ 2² 2¹ 2º

16 8 4 2 1
1
1
0
0
0
0
1
1
0
0 X X X X X

0
0
2
2
16
16
18
18
0
0
0
0

1.1.5 27 26 25 24 2³ 2² 2¹ 2º

128 64 32 16 8 4 2 1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0 X X X X X X X X

226
226
128
128
64
64
32
32
0
0
0
0
0
0
2
2
0
0

1.1.6
28
28
156
156
28
28
28
28
12
12
4
4
0
0
0
0 ˅ ˅ ˅ ˅ ˅ ˅ ˅ ˅ 27 26 25 24 2³ 2² 2¹ 2º

128 64 32 16 8 4 2 1
10011100
10011100
1
1 0 0
0
0
1
1
1
1
1
1
0
0
0
0 X X X X X X X X

156
156
128
128
0
0
0
0
16
16
8
8
4
4
0
0
0
0

1.1.7
127
127
255
255
63
63
31
31
15
15
7
7
1
1
3
3 ˅ ˅ ˅ ˅ ˅ ˅ ˅ ˅ 27 26 25 24 2³ 2² 2¹ 2º

128 64 32 16 8 4 2 1
11111111
11111111
1
1 1 1
1
1
1
1
1
1
1
1
1
1
1
1 X X X X X X X X

255
255
128
128
64
64
32
32
16
16
8
8
4
4
2
2
1
1

1.1.8
72
72
200
200
8
8
8
8
8
8
0
0
0
0
0
0 ˅ ˅ ˅ ˅ ˅ ˅ ˅ ˅ 27 26 25 24 2³ 2² 2¹ 2º

128 64 32 16 8 4 2 1
11001000
11001000
1
1 1 1
0
0
0
0
1
1
0
0
0
0
0
0 X X X X X X X X

200
200
128
128
64
64
0
0
0
0
8
8
0
0
0
0
0
0

*1.1.9
10012 = 9
*1.1.10
101110012 = 185
*1.1.11
1011112 = 47
*1.1.12
100000012 = 129
Review
1.
127
127
127
127
63
63
31
31
15
15
7
7
1
1
3
3 ˅ ˅ ˅ ˅ ˅ ˅ ˅ ˅ 27 26 25 24 2³ 2² 2¹ 2º

128 64 32 16 8 4 2 1
01111111
01111111
0
0 1 1
1
1
1
1
1
1
1
1
1
1
1
1 X X X X X X X X

255
255
0
0
64
64
32
32
16
16
8
8
4
4
2
2
1
1

I used the subtraction method by first finding the largest bit I could subtract from the decimal and proceeding with each bit after.
2.
102 and 00102 are equivalent because the two 0’s indicate that the bits are turned off and represent no value. Since both values have the same bits on and all other bits in each value are off they are equal.
3.
Base 5 is the same process (base 2 in binary) as other bases but the number is now a 5. For example, where base 2 (from right to left) is 20, 21, 22, 23, base 5 is 50, 51, 52, 53. The available digits are 0, 1, 2, 3, 4 and the first four digits of base 5 are 1, 5, 25, 125.
4.
Excel requires you to tell it which function is to be used and which cells to perform this function on. It would be difficult to tell Excel which bits to turn on, which to leave off and to carry the remainder over to the next bit. This also makes it difficult to tell it whether or not to perform a function based on the fact of whether or not the decimal is larger than any given bit.