Question

1. Convert to binary and hexadecimal (PLEASE SHOW WORK)

a. 35

- binary:

- hexadecimal:

b. 85

- binary:

- hexadecimal:

c. 128

- binary:

- hexadecimal:

d. 4563

- binary:

- hexadecimal:

Answer 1

a. 35
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.
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.
( 35 )10 = ( 100011 )2
Prepend zeros to make it 8-bit
( 35 )10 = ( 00100011 )2


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

Split 8-bit binary to 2 halves then Use above table to convert 4 bit binary to hex values
0010 in hex is 2
0011 in hex is 3
Answer in hex is (23)16

- binary: 100011
- hexadecimal: 23

=============================

b. 85
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.
85 /  2  result 42 remainder  1
42 /  2  result 21 remainder  0
21 /  2  result 10 remainder  1
10 /  2  result 5  remainder  0
5  /  2  result 2  remainder  1
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1
Read the remainders from bottom to top.
( 85 )10 = ( 1010101 )2
Prepend zeros to make it 8-bit
( 85 )10 = ( 01010101 )2

Split 8-bit binary to 2 halves then Use above table to convert 4 bit binary to hex values
0101 in hex is 5
0101 in hex is 5
Answer in hex is (55)16

- binary: 1010101
- hexadecimal: 55

=============================

c. 128
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.
128    /  2  result 64 remainder  0
64 /  2  result 32 remainder  0
32 /  2  result 16 remainder  0
16 /  2  result 8  remainder  0
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.
( 128 )10 = ( 10000000 )2

Split 8-bit binary to 2 halves then Use above table to convert 4 bit binary to hex values
1000 in hex is 8
0000 in hex is 0
Answer in hex is (80)16

- binary: 10000000
- hexadecimal: 80

=============================

d. 4563
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.
4563   /  2  result 2281   remainder  1
2281   /  2  result 1140   remainder  1
1140   /  2  result 570    remainder  0
570    /  2  result 285    remainder  0
285    /  2  result 142    remainder  1
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.
( 4563 )10 = ( 1000111010011 )2
Prepend zeros to make it 16-bit
( 4563 )10 = ( 0001000111010011 )2

Split 8-bit binary to 2 halves then Use above table to convert 4 bit binary to hex values
0001 in hex is 1
0001 in hex is 1
1101 in hex is D
0011 in hex is 3
Answer in hex is (11D3)16


- binary: 1000111010011
- hexadecimal: 11D3