1155 - Problem F: Geek Challenge [SKRZAT] (Base Minus Two)

Time Limit : 1 Second

Memory Limit : 128 MB

Submission: 30

Solved: 18

Description

Geek Challenge [SKRZAT] is an old, old game from Poland that uses a game console with two
buttons plus a joy stick. As is true to its name, the game communicates in binary, so that one
button represents a zero and the other a one. Even more true to its name, the game chooses to
communicate so that the base of the number system is minus two, not plus two, so we’ll call this
representation “Weird Binary”. Thus the bit positions label the powers of minus two, as seen in
the following five-bit tables:
Bits Value Bits Value Bits Value Bits Value
00000 0 01000 -8 10000 16 11000 8
00001 1 01001 -7 10001 17 11001 9
00010 -2 01010 -10 10010 14 11010 6
00011 -1 01011 -9 10011 15 11011 7
00100 4 01100 -4 10100 20 11100 12
00101 5 01101 -3 10101 21 11101 13
00110 2 01110 -6 10110 18 11110 10
00111 3 01111 -5 10111 19 11111 11
Bits Value Bits Value Bits Value Bits Value
01010 -10 00010 -2 11010 6 10010 14
01011 -9 00011 -1 11011 7 10011 15
01000 -8 00000 0 11000 8 10000 16
01001 -7 00001 1 11001 9 10001 17
01110 -6 00110 2 11110 10 10110 18
01111 -5 00111 3 11111 11 10111 19
01100 -4 00100 4 11100 12 10100 20
01101 -3 00101 5 11101 13 10101 21
Numbers are presented on the screen in Weird Binary, and then numbers are accepted in
response from the console as a stream of zeroes and ones, terminated by a five-second pause.
You are writing a computer program to support the novice geek in playing the game by
translating numbers between decimal and Weird Binary.

Input

The first line in the file gives the number of problems being posed without any white space.
Following are that many lines. Each line will either be a conversion into Weird Binary or out of
Weird Binary: the letter "b" indicates that the rest of the line is written in Weird Binary and
needs to be converted to decimal; the letter "d" indicates that the rest of the line is written in
decimal and needs to be converted to Weird Binary.
The input data are in the range to fit within a 15-bit Weird Binary number, which represents the
decimal number range –10922 to 21845, inclusive.

Output

For each conversion problem, show the type of problem, its input string, and the converted result
in the format shown below, replicating even the spacing exactly as shown. Leading zeroes are
not allowed.

sample input

10 
b 1001101 
b 0111111 
b 101001000100001 
b 010010001000010 
b 100110100110100 
d -137 
d 137 
d 8191 
d -10000 
d 21000

sample output

From binary: 1001101 is 61 
From binary: 0111111 is -21 
From binary: 101001000100001 is 19937 
From binary: 010010001000010 is -7106 
From binary: 100110100110100 is 15604 
From decimal: -137 is 10001011 
From decimal: 137 is 110011001 
From decimal: 8191 is 110000000000011 
From decimal: -10000 is 10100100110000 
From decimal: 21000 is 101011000011000

hint

source