Question

Q1: Translate the following Bytes to Decimal and Hexadecimal

a) 00001001

b) 111111111

c) 11101110

d) 01010101

Answer 1

a) 00001001
Decimal:
1     *  2^0    =  1  *  1  =  1
0     *  2^1    =  0  *  2  =  0
0     *  2^2    =  0  *  4  =  0
1     *  2^3    =  1  *  8  =  8
sum = 1 + 0 + 0 + 8 = 9

( 1001 )2 = ( 9 )10

Hexadecimal:

1001

9

( 1001 )₂ = ( 9 )₁₆

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

b) 111111111
Decimal:
1     *  2^0    =  1  *  1  =  1
1     *  2^1    =  1  *  2  =  2
1     *  2^2    =  1  *  4  =  4
1     *  2^3    =  1  *  8  =  8
1     *  2^4    =  1  *  16 =  16
1     *  2^5    =  1  *  32 =  32
1     *  2^6    =  1  *  64 =  64
1     *  2^7    =  1  *  128    =  128
1     *  2^8    =  1  *  256    =  256
sum = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 = 511
( 111111111 )2 = ( 511 )10

Hexadecimal:

0001	1111	1111
1	F	F

( 111111111 )₂ = ( 1FF )₁₆

====================================
c) 11101110
Decimal:
0     *  2^0    =  0  *  1  =  0
1     *  2^1    =  1  *  2  =  2
1     *  2^2    =  1  *  4  =  4
1     *  2^3    =  1  *  8  =  8
0     *  2^4    =  0  *  16 =  0
1     *  2^5    =  1  *  32 =  32
1     *  2^6    =  1  *  64 =  64
1     *  2^7    =  1  *  128    =  128
Sum = 0 + 2 + 4 + 8 + 0 + 32 + 64 + 128 = 238
( 11101110 )2 = ( 238 )10


Hexadecimal:

1110	1110
E	E

( 11101110 )₂ = ( EE )₁₆

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

d) 01010101
Decimal:
1     *  2^0    =  1  *  1  =  1
0     *  2^1    =  0  *  2  =  0
1     *  2^2    =  1  *  4  =  4
0     *  2^3    =  0  *  8  =  0
1     *  2^4    =  1  *  16 =  16
0     *  2^5    =  0  *  32 =  0
1     *  2^6    =  1  *  64 =  64
Sum = 1 + 0 + 4 + 0 + 16 + 0 + 64 = 85
( 1010101 )2 = ( 85 )10

Hexadecimal:

0101	0101
5	5

( 1010101 )₂ = ( 55 )₁₆