Question

Convert from binary to decimal to hexadecimal (PLEASE SHOW ALL WORK)

a. 1010 1011

- decimal:

- hexadecimal

b. 0011 0001

- decimal:

- hexadecimal:

c. 1110 0111

- decimal:

- hexadecimal:

d. 1111 1111

- decimal:

- hexadecimal:

Answer 1

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
Use this table when converting to hexadecimal

a)  1010 1011
=>  1x2^7 + 0x2^6 + 1x2^5 + 0x2^4 + 1x2^3 + 0x2^2 + 1x2^1 + 1x2^0
=>  1x128 + 0x64 + 1x32 + 0x16 + 1x8 + 0x4 + 1x2 + 1x1
=>  128 + 0 + 32 + 0 + 8 + 0 + 2 + 1
=>  171
in decimal it is 171
1010 is A
1011 is B
in hexadecimal it is AB

b)  0011 0001
=>  0x2^7 + 0x2^6 + 1x2^5 + 1x2^4 + 0x2^3 + 0x2^2 + 0x2^1 + 1x2^0
=>  0x128 + 0x64 + 1x32 + 1x16 + 0x8 + 0x4 + 0x2 + 1x1
=>  0 + 0 + 32 + 16 + 0 + 0 + 0 + 1
=>  49
in decimal it is 49
0011 is 3
0001 is 1
in hexadecimal it is 31

c)  1110 0111
=>  1x2^7 + 1x2^6 + 1x2^5 + 0x2^4 + 0x2^3 + 1x2^2 + 1x2^1 + 1x2^0
=>  1x128 + 1x64 + 1x32 + 0x16 + 0x8 + 1x4 + 1x2 + 1x1
=>  128 + 64 + 32 + 0 + 0 + 4 + 2 + 1
=>  231
in decimal it is 231
1110 is E
0111 is 7
in hexadecimal it is E7

d)  1111 1111
=>  1x2^7 + 1x2^6 + 1x2^5 + 1x2^4 + 1x2^3 + 1x2^2 + 1x2^1 + 1x2^0
=>  1x128 + 1x64 + 1x32 + 1x16 + 1x8 + 1x4 + 1x2 + 1x1
=>  128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
=>  255
in decimal it is 255
1111 is F
1111 is F
in hexadecimal it is FF