Hexadecimal and binary together
Answers are for parents and teachers.
1
Convert (5E)₁₆ to binary, without leading zeros.
5 = 0101 and E = 1110, so 01011110, which is 1011110.
2
Convert 111001011 to hexadecimal.
From the right: 1 1100 1011 gives, with padding, 0001 | 1100 | 1011, so 1CB.
3
Convert 3000 to hexadecimal and check it by multiplying back.
3000 ÷ 16 = 187 r 8; 187 ÷ 16 = 11 r 11 (B); 11 ÷ 16 = 0 r 11 (B). The answer is BB8. Check: 11×256 + 11×16 + 8 = 2816 + 176 + 8 = 3000.
4
Write the byte 01111011 as two hexadecimal symbols.
0111 = 7 and 1011 = B, so 7B.
5
A student converts (A3)₁₆ to 101011. Find the mistake and give the right answer.
The 3 must be written with four bits, 0011, not 11. The right answer is 1010 0011, that is 10100011. (101011 is only 43; A3 is 163.)