PHYS345 Electricity and Electronics

Hint for D9.3

For longer binary numbers, it is usually helpful to first convert to hex and then use the power-of-16 placeholders to make the conversion. For example, 11 1010 0110 = 3A6H.

Hint for D9.4

One way to convert decimal to binary is to perform successive divisions by 2, checking for an odd or even number at each step. If odd, then record a 1 for the bit, and subtract one from the quotient. If even, then record a 0 for the bit. Continue dividing by 2 until the number become fractional.

For example:
  2001 odd 1 least significant digit
sub 1, div 2 1000 even 0
div 2 500 even 0
div 2 250 even 0
div 2 125 odd 1
sub 1, div 2 62 even 0
div 2 31 odd 1
sub 1, div 2 15 odd 1
sub 1, div 2 7 odd 1
sub 1, div 2 3 odd 1
sub 1, div 2 1 odd 1 most significant digit

Answer: 0111 1101 0001

Alternatively, convert 200010 first to hex, then that number (7D1H) to binary.

Hint for D9.5

In binary, 1 + 1 + 1 = 11 
That is, 1 carry 1.

Hint for D9.10

For binary to hex conversion, go from right to left setting up groups of 4 bits, then associate the appropriate hex digit with each nibble.

Hint for P9-2

0 1100   binary representation of 1210
1 0011   one's complement
+ 1   add one to find the
1 0100   two's complement

Hint for P9.3

The two's complement of 0 1111 (15) is 1 0001.
The two's complement of 1 0011 (3) is 1 1101.


"http://www.physics.udel.edu/~watson/phys345/protected/exercises/hints/1022.html"
Last updated Oct. 24, 1998.
Copyright George Watson, Univ. of Delaware, 1998.