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 (0101 1001 ), to a decimal expansion. 2. (3 points) - Convert the following decimal expansion ( 124 ).o to an 8-bit binary expansion. 3. (2 points) - Convert the following hexadecimal expansion (D40 16 to an octal expansion. 4. (2 points) - Convert the following binary expansion ( 1001 1010 0101 1001 ), to a hexadecimal expansion.

Answer 1

✔Solution(1)

(0101 1001)₂ = (?)₁₀

Start from right and multiply each bit with the power of 2 (starts from 0 to n-1)

1*2⁰ +0*2¹ + 0*2²+1*2³​​​​+1*2⁴​​​​​+0*2⁵+1*2⁶​​​​​​+0*2⁷​

= 1*1 +0 +0+1*8+1*16+0+1*64+0

=1+8+16+64

= 89

The Answer is (89)₁₀​​​​​​

✔Solution(2)

(124)₁₀ = (?)₂

(124 ) = 0*2⁰ +0*2¹ + 1*2²+1*2³​​​​+1*2⁴​​​​​+1*2⁵+1*2⁶​​​​​​

The answer is (111100)₂

✔Solution(3)

(D40)₁₆ = (?)₈

In hexadecimal A = 10, B= 11, C= 12, D=13, E = 14, F = 15

So put the corresponding value of D

(13 40)₁₆

Now Convert 13 and 40 to binary

13 = 1*2⁰ +0*2¹+1*2²+1*2³ = 1101

4 = 0*2⁰ +0*2¹+1*2²

4 = 0100

0 =0000

Now put both values together

(13 40)₁₆ = (110101000000)₂

Now make a pair of three

(110101000000)₂

Now again convert each pair into decimal

110 = 6

101= 5

000= 0

000= 0

Now put these values

The answer is (6500)₈

✔Solution(4)

(1001 1010 0101 1001)₂

Now convert each pair into decimal

1001 = 9

1010 = 10 = A

0101 = 5

1001 =9

So the Answer is (9A59)₁₆

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