Directions: Complete all problems. Write down all steps. Show all work. Do not u
ID: 3744453 • Letter: D
Question
Directions: Complete all problems. Write down all steps. Show all work. Do not use online digit converter. Box your final answers. Write neatly! Staple your paper in the upper-left hand corner. 1. Convert the following numbers a) 100111000001111012X10 b) 0000101100002 =X10 1001011010012-X8 d) 1000112-X8 e) 1000010112=X16 f) 101001001001012-X16 g) 475648-X2 h) 13618=X2 i) A2F016-X2 j) 3FID16-X2 k) 74128 X16 1) 13658-X16 m) D36AC16 Xg n) DCBA 16 X8 2. Convert the following numbers using the division method. Be sure to show all the steps. a) 41210-X2 b) 340110-X2 4289910-X16 d) 551010-X16 e) 999810 X8 f) 729010-X8 3. Convert the following unsigned fraction numbers a) 47.562510 X2 110000.00 100112 1011001.0112-X16 c)Explanation / Answer
Question 1a
( 10011100000111101 )2 = (?)10
( 10011100000111101 )2 = ( 79933 )10
Explanantion
1
*
20
=
1
*
1
=
1
0
*
21
=
0
*
2
=
0
1
*
22
=
1
*
4
=
4
1
*
23
=
1
*
8
=
8
1
*
24
=
1
*
16
=
16
1
*
25
=
1
*
32
=
32
0
*
26
=
0
*
64
=
0
0
*
27
=
0
*
128
=
0
0
*
28
=
0
*
256
=
0
0
*
29
=
0
*
512
=
0
0
*
210
=
0
*
1024
=
0
1
*
211
=
1
*
2048
=
2048
1
*
212
=
1
*
4096
=
4096
1
*
213
=
1
*
8192
=
8192
0
*
214
=
0
*
16384
=
0
0
*
215
=
0
*
32768
=
0
1
*
216
=
1
*
65536
=
65536
On adding all the result
1 + 0 + 4 + 8 + 16 + 32 + 0 + 0 + 0 + 0 + 0 + 2048 + 4096 + 8192 + 0 + 0 + 65536 = 79933
Question 1b
( 000010110000 )2 = ( ?)10
( 000010110000 )2 = ( 176 )10
Explanation
0
*
20
=
0
*
1
=
0
0
*
21
=
0
*
2
=
0
0
*
22
=
0
*
4
=
0
0
*
23
=
0
*
8
=
0
1
*
24
=
1
*
16
=
16
1
*
25
=
1
*
32
=
32
0
*
26
=
0
*
64
=
0
1
*
27
=
1
*
128
=
128
On adding al the result
0 + 0 + 0 + 0 + 16 + 32 + 0 + 128 = 176
Question 1c
(100101101001)2 = (?)8
While converting from binary to octal we will group the binary number into three and put there corresponding value for octal
100 101 101 001
(4551)8
Question 1d
(100011)2 = (?)8
While converting from binary to octal we will group the binary number into three and put there corresponding value for octal
100 011
(43)8
Question 1e
(100001011)2 = (?)16
While converting from binary to hexadecimal we will group the binary number into four and put there corresponding value for hexadecimal
0001 0000 1011
(10B)16
Question 1f
(10100100100101)2 = (?)16
While converting from binary to hexadecimal we will group the binary number into four and put there corresponding value for hexadecimal
0010 1001 0010 0101
(2925)16
Question 1g
(47564)8 = (?)2
While converting from octal to binary we will convert each digit to binary and group them each into three and join them.
47564
100 111 101 110 100
(100111101110100)2
Question 1h
(1361)8 = (?)2
While converting from octal to binary we will convert each digit to binary and group them each into three and join them.
1361
001 011 110 001
(001011110001)2
Question 1i
(A2F0)16 = (?)2
While converting from hexadecimal to binary we will convert each digit to binary and group them each into four and join them.
A2F0
1010 0010 1111 0000
(1010001011110000)2
Question 1j
(3F1D)16 = (?)2
While converting from hexadecimal to binary we will convert each digit to binary and group them each into four and join them.
3F1D
0011 1111 0001 1101
(0011111100011101)2
1
*
20
=
1
*
1
=
1
0
*
21
=
0
*
2
=
0
1
*
22
=
1
*
4
=
4
1
*
23
=
1
*
8
=
8
1
*
24
=
1
*
16
=
16
1
*
25
=
1
*
32
=
32
0
*
26
=
0
*
64
=
0
0
*
27
=
0
*
128
=
0
0
*
28
=
0
*
256
=
0
0
*
29
=
0
*
512
=
0
0
*
210
=
0
*
1024
=
0
1
*
211
=
1
*
2048
=
2048
1
*
212
=
1
*
4096
=
4096
1
*
213
=
1
*
8192
=
8192
0
*
214
=
0
*
16384
=
0
0
*
215
=
0
*
32768
=
0
1
*
216
=
1
*
65536
=
65536
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