Question

In the following problems, you are asked to convert from one number base to another. I am aware that there are calculators that will do this for you. Thus, you must show all your work to get credit for these problems.

1. (3 points) – Convert the 8-binary binary expansion ( 0110 1001 )2 to a decimal expansion.

2. (3 points) – Convert the following decimal expansion (142)10 to an 8-bit binary expansion.

3. (2 points) – Convert the following hexadecimal expansion (4AD)16 to an octal expansion.

4. (2 points) – Convert the following binary expansion ( 1001 1010 0110 0101 )2 to a hexadecimal expansion.

Answer 1

1.

1 * 0 1 2 * 23 = : : : | = = - 1 0 0 1 0 1 1 + 1 + 2 + 4 + 8 + 16 x 32 * 64 : : 0 8 = 32 1 1 + 25 * 26

Add together all products

1 + 0 + 0 + 8 + 0 + 32 + 64 = 105

Answer: 105

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2.

Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

142 /  2  result 71 remainder  0
71 /  2  result 35 remainder  1
35 /  2  result 17 remainder  1
17 /  2  result 8  remainder  1
8  /  2  result 4  remainder  0
4  /  2  result 2  remainder  0
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1

Read the remainders from bottom to top.

( 142 )₁₀ = ( 10001110 )₂

Answer: 10001110

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3.

0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
0000	0001	0010	0011	0100	0101	0110	0111	1000	1001	1010	1011	1100	1101	1110	1111

Given number is 4AD

4	A	D
0100	1010	1101

( 4AD )₁₆ = ( 10010101101 )₂

Convert each 3 bit of binary to octal using below table

Octal     Binary
-------------------------
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

So, answer is 2255

Answer: 2255

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4.

convert each 4 bit to its hexa value

1001	1010	0110	0101
9	A	6	5

( 1001101001100101 )₂ = ( 9A65 )₁₆

Answer: 9A65