Question

Convert the following binary numbers to decimal (6 points):
11111
101011
1101011

Convert the following decimal numbers to binary (6 points):
49
367
1023

Convert the following hex numbers to decimal (4 points):
ACE
800

Convert the following decimal numbers to hex (4 points):
64,206
16,383

If b is a binary number, what number is represented by b0? That is, what number do you get when you place a 0 at the end of a binary number? What happens if you place two 0's at the end? Generalize your answer: what happens if you place n 0's at the end? (3 points)

Determine the binary representation of the following integers using 8 bits (6 points):
-15
-64
-127

Answer 1

1). binary to decimal
11111 = 2^4 2^3 2^2 2^1 2^0 = 16+8+4+2+1 = 31
Ans. 31

101011 = 43

1101011 = 107

2). decimal to binary
49 = 00110001
367 = 0000000101101111
1023 = 0000001111111111

3). Hex to decimal
ACE = 2766
800 = 2048

4). Decimal to hex
64,206 = FACE
16,383 = 3FFF


5). Binary using octal
-15 = -1101
-64 = -110100
-127 = -1010111