Complete the missing entries in the table below.
Decimal Binary Quaternary Octal Hexadecimal
654.625 1010001110.101 22032.22 1216.5 28E.A
54.875 110110.111 312.32 66.7 36.E
57.25 111001.01 321.1 71.2 39.4
43.375 101011.011 223.12 53.3 2B.6
2989.80078125 101110101101.11001101 232231.3031 5655.632 BAD.CD

Complete the following table concerning the smallest and largest integers that can be represented in a 5-bit configuration given the different storage modes.
Storage Mode Decimal (Base-10) Binary (Base-2)
Smallest Largest Smallest Largest
Unsigned 0 25-1=31 00000 11111
Sign Magnitude -25-1+1=-15 25-1-1=15 11111 01111
One's Complement -25-1+1=-15 25-1-1=15 10000 01111
Two's Complement -25-1=-16 25-1-1=15 10000 01111

Complete the following table. For each of the internal forms shown in the first column, provide the decimal (base-10) equivalent assuming numbers are stored in the various storage modes.
Internal
Representation		 Storage Mode
Unsigned Sign
Magnitude		 One's
Complement		 Two's
Complement
0101 1001 89 +89 +89 +89
1010 0110 166 -38 -89 -90
1111 1111 255 -127 -0 -1
1000 0000 128 -0 -127 -128

Complete the following table. For each of the decimal numbers shown in the first column, provide the internal representation assuming numbers are stored in the various storage modes. Assume an 8-bit word size.
Decimal
Number		 Storage Mode
Unsigned Sign
Magnitude		 One's
Complement		 Two's
Complement
-129 Invalid Invalid Invalid Invalid
-128 Invalid Invalid Invalid 1000 0000
-127 Invalid 1111 1111 1000 0000 1000 0001
-23 Invalid 1001 0111 1110 1000 1110 1001
-1 Invalid 1000 0001 1111 1110 1111 1111
-0 Invalid 1000 0000 1111 1111 Invalid
0 0000 0000 0000 0000 0000 0000 0000 0000
1 0000 0001 0000 0001 0000 0001 0000 0001
23 0001 0111 0001 0111 0001 0111 0001 0111
127 0111 1111 0111 1111 0111 1111 0111 1111
128 1000 0000 Invalid Invalid Invalid
255 1111 1111 Invalid Invalid Invalid
256 Invalid Invalid Invalid Invalid


Mark B. Motl
mmotl@cs.angelo.edu