Please complete the following tasks to signify your successful completion of Uni

Question

Please complete the following tasks to signify your successful completion of Unit 4. Save your work into a word document. Upload your answers using the buttons below to this page to post me your document. Write each of the following decimal values in binary. (Don't just jot down the answer: please show the arithmetic you used to perform the conversion.) Write each of the following binary values in decimal. (Don't just jot down the answer: please show the arithmetic you used to perform the conversion.) Write each of the following binary values in hexadecimal. (Don't just jot down the answer: please show the process you used to perform the conversion.) Write each of the following hexadecimal values in binary. (Don't just jot down the answer: please show the process you used to perform the conversion.) Write each of the following hexadecimal values in decimal. (Don't just jot down the answer: please show the process you used to perform the conversion.)

Explanation / Answer

Converting decimal values in binary with divide by 2 algorithm. Decimal Number is divided by 2 and the remainder is stored; again the quotient is divided by 2 and the remainder is stored; this process repeats until quotient becomes 0 :

Decimal value: 57.

57/2=28 remainder =1

28/2=14 remainder =0

14/2= 7 remainder =0

7/2=3 remainder =1

3/2=1 remainder =1

1/2= 0 remainder =1

Now read the remainder from bottom to top like: 111001; it is the binary equivalent of 57.

So (57)10 = (111001)2

Decimal value: 24.

24/2=12 remainder= 0

12/2=6 remainder= 0

6/2= 3 remainder= 0

3/2=1 remainder= 1

1/2= 0 remainder= 1

Now read the remainder from bottom to top like: 11000; it is the binary equivalent of 24.

So (24)10 = (11000)2

Decimal value: 93.

93/2=46 remainder =1

46/2=23 remainder =0

23/2= 11 remainder =1

11/2=5 remainder =1

5/2=2 remainder =1

2/2= 1 remainder =0

1/2 = 0 remainder =1

Now read the remainder from bottom to top like: 1011101; it is the binary equivalent of 93.

So (93)10 = (1011101)2

Decimal value: 141.

141/2=70 remainder =1

70/2=35 remainder =0

35/2= 17 remainder =1

17/2=8 remainder =1

8/2=4 remainder =0

4/2= 2 remainder =0

2/2= 1 remainder =0

1/2 = 0 remainder =1

Now read the remainder from bottom to top like: 10001101; it is the binary equivalent of 141.

So (141)10 = (10001101)2

Decimal value: 48.

48/2=24 remainder =0

24/2=12 remainder= 0

12/2=6 remainder= 0

6/2= 3 remainder= 0

3/2=1 remainder= 1

1/2= 0 remainder= 1

Now read the remainder from bottom to top like: 110000; it is the binary equivalent of 48.

So (48)10 = (110000)2

Converting binary values in decimal:

(1001011) 2 = 1*26 + 0*25 + 0*24 + 1*23 + 0*22 + 1*21 + 1*20 = 75

(1100001)2 = 1*26 + 1*25 + 0*24 + 0*23 + 0*22 + 0*21 + 1*20 = 97

(11101000)2 = 1*27 + 1*26 + 1*25 + 0*24 + 1*23 + 0*22 + 0*21 + 0*20 =232

(1001111) 2 = 1*26 + 0*25 + 0*24 + 1*23 + 1*22 + 1*21 + 1*20 = 79

(101100101) 2 = 1*28 + 0*27 + 1*26 + 1*25 + 0*24 + 0*23 + 1*22 + 0*21 + 1*20 = 357

Converting binary to hexadecimal:

Step 1: cut binary numbers into groups of four, starting from the right.

Step 2: Add extra zeros to the front of the first number if it is not four digits.

Step 3: Convert one 4-digit group at a time( in hex after 9 it is A,B,C,D,E and F)

(10111001)2 = (1011)(1001) = (1*23 + 0*22 + 1*21 + 1*20) (1*23 + 0*22 + 0*21 + 1*20) = (11)(9) = B9

(10111001)2 is equal to B9 in Hex.

(01110001)2 = (0111)(0001) = (0*23 + 1*22 + 1*21 + 1*20) (0*23 + 0*22 + 0*21 + 1*20) = (7)(1) = 71

(01110001)2 is equal to 71 in Hex.

(1000001)2 = (0100)(0001) = (0*23 + 1*22 + 0*21 + 0*20) (0*23 + 0*22 + 0*21 + 1*20) = (4)(1) = 41

(1000001)2 is equal to 41 in Hex.

(11101001)2= (1110)(1001) = (1*23 + 1*22 + 1*21 + 0*20) (1*23 + 0*22 + 0*21 + 1*20) = (14)(9) = E9

(11101001)2 is equal to E9 in Hex.

(1001010101)2 =(0010)(0101)(0101) = (0*23 + 0*22 + 1*21 + 0*20) (0*23 + 1*22 + 0*21 + 1*20) (0*23 + 1*22 + 0*21 + 1*20) = (2)(5)(5)=255

(1001010101)2 is equal to 255 in Hex.

Converting hexadecimal to binary:

Step 1: Convert each hexadecimal digit to a 4-digit binary number.

Step 2: Combine all the resulting binary groups (of 4 digits each) into a single binary number.   

(DEED)16 = (13)10(14)10(14)10(13)10 = (1101)2(1110)2(1110)2(1101)2 =(1101111011101101)2

(BEED)16 = (11)10(14)10(14)10(13)10 = (1011)2(1110)2(1110)2(1101)2 =(1011111011101101)2

(CEE)16 = (12)10(14)10(14)10= (1100)2(1110)2(1110)2=(110011101110)2

(345)16 = (3)10(4)10(5)10= (0011)2(0100)2(0101)2=(001101000101)2

Converting hexadecimal to decimal:

(BEEF)16 = 11 * 163 + 14 * 162 + 14 * 161 + 15 * 160 = 48879

(BAD)16 = 11 * 162 + 10 * 161 + 13 * 160 = 2989

(FAD)16 = 15 * 162 + 10 * 161 + 13 * 160 = 4013

(456)16 = 4 * 162 + 5 * 161 + 6 * 160 = 1110

(DEF)16 = 13 * 162 + 14 * 161 + 15 * 160 = 3567

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