(2013, c ) http://istksckwanseiacjp/ ishiura/lc/ 1 2, 8, 16 2 10 (2 ) 11 2, 8, 16 10 (decimal) 1192 10 = 1 10 3 + 1 10 2 + 9 10 1 + 2 10 0 (a n 1 a n 2 a 1 a 0 ) 10 = 8 (octal) n 1 i=0 a i 10 i 710 8 = 7 8 2 + 1 8 1 + 0 8 0 = 456 10 n 1 (a n 1 a n 2 a 1 a 0 ) 8 = 2 (binary) i=0 a i 8 i 1110 2 = 1 2 3 + 1 2 2 + 1 2 1 + 0 2 0 = 14 10 n 1 (a n 1 a n 2 a 1 a 0 ) 2 = i=0 a i 2 i 2 1 ( bit ) 16 ( hexadecimal ) 0,1,2,3,4,5,6,7,8,9, A, B, C, D, E, F,10,11,12,13, AE86 16 = 10 16 3 + 14 16 2 + 8 16 1 + 6 16 0 = 44678 10 (a n 1 a n 2 a 1 a 0 ) 16 = r n 1 i=0 n 1 (a n 1 a n 2 a 1 a 0 ) r = a i 16 i i=0 a i r i r ( radix ) 1 1
11 n ( ) 2 x n 0 x 4 0 x 8 0 x 16 0 x 32 0 x { n }} { 111111 11 2 ( 2 n 1 ) 4 1111 2 ( 15 10 ) 8 11111111 2 ( 255 10 ) 16 111111 11 2 (65,535 10 ) 32 111111 11 2 (4,294,967,295 10 ) 11 10 2816 5 101 5 5 7 111 7 7 8 1000 10 8 13 1101 15 D 15 1111 17 F 16 10000 20 10 31 11111 37 1F 32 100000 40 20 1 2
12 2, 8, 16 8 8 = 2 3, 8 1 2 3 2573 8 = 010 101 111 011 2 = 10101111011 2 1101101001111 2 = 1 101 101 001 111 2 = 15517 8 16 16 = 2 4, 16 1 2 4 7A6D 16 = 0111 1010 0110 1101 2 = 111101001101101 2 11101101001111 2 = 11 1011 0100 1111 2 = 3B4F 16 10 /16 2 10 /16 2 10 16 2 10 16 2 0 0000 4 0100 8 8 1000 12 C 1100 1 0001 5 0101 9 9 1001 13 D 1101 2 0010 6 0110 10 A 1010 14 E 1110 3 0011 7 0111 11 B 1011 15 F 1111 8 16,, (0 1 ) ) KGU 01001011 01000111 01010101 2 4B4755 16 12 2 8 16 10110101 265 B5 11010111110 3276 6BE 101000111111 5077 A3F 1 3
13 2 10 11 2 110101 2 10 [ 1] 110101 2 = 1 2 5 + 1 2 4 + 0 2 3 + 1 2 2 + 0 2 1 + 1 2 0 = 32 + 16 + 4 + 1 = 53 [ 2] 2 2 6 12 26 52 1 1 0 1 0 1 2 + 2 + 2 1 3 6 13 26 53 + 2 + 2 + 13 2 111011011 2 10 10 0 10, 2 0, 2, 110 2 = 6 10, 110 2 0 1100 2, 6 2 = 12, 110 2 1 1101 2, 1100 2 + 1, 6 2 + 1 = 13 1100 2 = 110 2 2 + 0 = 12 1101 2 = 110 2 2 + 1 = 13, 2 10 110101 2, 1 2 = 1 11 2 = 1 2 2 + 1 = 3 110 2 = 11 2 2 + 0 = 6 1101 2 = 110 2 2 + 1 = 13 11010 2 = 1101 2 2 + 0 = 26 110101 2 = 11010 2 2 + 1 = 53, 2,,, 2 10,, (a 5 a 4 a 3 a 2 a 1 a 0 ) 2 = a 5 2 5 + a 4 2 4 + a 3 2 3 + a 2 2 2 + a 1 2 + a 0 = (((((a 5 ) 2 + a 4 ) 2 + a 3 ) 2 + a 2 ) 2 + a 1 ) 2 + a 0 (Horner s rule) 1 4
14 10 2 12 10 53 2 [ 1] n 0 1 2 3 4 5 6 7 2 n 1 2 4 8 16 32 64 128 53 = 32 + 21 = 32 + 16 + 5 = 32 + 16 + 4 + 1 = 2 5 + 2 4 + 2 2 + 2 0 = 110101 2 [ 2] 2 2 2 2 2 2 0 1 3 6 13 26 53 1 1 0 1 0 1 ( ) 14 10 397 10 2 2 0, 0, 2 6 10 = 110 2 11 2 = 3 10, 2 1, 1, 2 ( ) 7 10 = 111 2 11 2 = 3 10, 2, 2 53/2 =26 1 53 =?????1 2????? 26 2 26/2 =13 0 53 =????01 2???? 13 2 13/2 = 6 1 53 =???101 2??? 6 2 6/2 = 3 0 53 =??0101 2?? 3 2 3/2 = 1 1 53 =?10101 2? 1 2 1/2 = 0 1 53 = 110101 2, a 0,a 1,,a 6 (a 5 a 4 a 3 a 2 a 1 a 0 ) 2 = a 5 2 5 + a 4 2 4 + a 3 2 3 + a 2 2 2 + a 1 2 + a 0 = (((((a 5 ) 2 + a 4 ) 2 + a 3 ) 2 + a 2 ) 2 + a 1 ) 2 + a 0 1 5
15 2 2 10 (, ) (0) (1) (0) (carry) 1 0 1 1 (11 10 ) +) 0 0 1 0 (2 10 ) 1 1 0 1 (13 10 ) (1) (1) (0) (borrow) 1 0 0 1 (9 10 ) ) 0 0 1 0 (2 10 ) 0 1 1 1 (7 10 ) 1 0 0 1 (9 10 ) ) 1 0 1 1 (11 10 ) 1 0 0 1 1 0 0 1 0 0 0 0 +) 1 0 0 1 1 1 0 0 0 1 1 (99 10 ) 1 1 ( 3 10 ) ( 3 10 ) 1 1 ) 1 0 1 1 ( 11 10 ) 1 1 1 0 1 1 1 1 0 ( 2 10 ) 1 6
16 161 n 2 02 n 1 ( ), 162 1 ( one s complement ) x 1, x (0 1, 1 0 ) ) 00010101 1 11101010 2 ( two s complement ) x 2, x 1 1 ) 01110110 1 10001001 2 1 1 10001010 163 3 (1) / ( sign magnitude ) n, n 1, 0, 1 ) 6 6 000110 6 100110 (2) 1 (one s complement) x 1 ) 6 6 000110 6 111001 (3) 2 (two s complement) x 2 ) 6 6 000110 6 111010 1 2 1 7
15 x 4 (n = 4) / 1 2 7 0111 0111 0111 6 0110 0110 0110 5 0101 0101 0101 4 0100 0100 0100 3 0011 0011 0011 2 0010 0010 0010 1 0001 0001 0001 0 0000 0000 0000 1 1001 1110 1111 2 1010 1101 1110 3 1011 1100 1101 4 1100 1011 1100 5 1101 1010 1011 6 1110 1001 1010 7 1111 1000 1001 8 1000 162, 8 2 (1000) 2 ( 0, 1 ) 2 2 10, 1 9999, 2 9998,, 10 9990 2 n x 2, 2 n x 2 (100 00 2 x), 4 0001 2 10000 0001 = 1111 0010 2 10000 0010 = 1110 1 n x 1, 2 n 1 x 2 ( 11 11 2 x) 2 1 1, n n 1 8
17 2 171 2 /10 13 10 2 (5 2 ) (1) 13 10 1310 2 01101 2 01101 10010 +1 10011 ( ) (2) 1 10 110 2 00001 2 00001 11110 +1 11111 ( ) (3) 13 10 ( 4 ), 2 13 10 = 01101 ( ) 16 10 2 (5 2 ) (1) 10 10 (2) 7 10 12 x 2 2 x ) x = 01101 2 10011 2 01101 14 2 11010 10 1 2 6, 6 17 2 11110 10 00110 2, 10 2 14 2, ( ) 2 ) 11010 = 1 ( 16) + 1 8 + 0 4 + 1 2 + 0 1 = 6 2 10, 1 1 2 2 4 6 1 1 0 1 0 1 1 2 3 6 1 9
172 2 13 2, n x n n 4 6 8 16 32 n 1000000 00 2 ( 2 n 1 n ) x 4 1000 2 ( 8 10 ) x 6 100000 2 ( 32 10 ) x 8 10000000 2 ( 128 10 ) x 16 10000 00 2 ( 32,768 10 ) x 0111111 11 2 ( 2 n 1 1 ) 4 0111 2 ( 7 10 ) 6 011111 2 ( 31 10 ) 8 01111111 2 ( 127 10 ) 16 01111 11 2 (32,767 10 ) 32 32 1000000 00 2 ( 2,147,483,648 10 ) x 0111111 11 2 (2,147,483,647 10 ) 2,, 2 (, ) 2 + 3 = 1110 + 0011 = 0001 = 1 (5 ) 7 + 3 = 1001 + 0011 = 1100 = 4, 10, 2 + 3 = 9998 + 0003 = 0001 7 + 3 = 9993 + 0003 = 9996 = 4 5 3 = 5 + ( 3) = 0101 + 1101 = 0010, 2,, 2 1 10
11 10 2816 5 101 5 5 7 111 7 7 8 1000 10 8 13 1101 15 D 15 1111 17 F 16 10000 20 10 31 11111 37 1F 32 100000 40 20 12 2816 10110101 265 B5 11010111110 3276 6BE 101000111111 5077 A3F 13 111011011 2 = 475 10 2 6 14 28 58 118 236 474 1 1 1 0 1 1 0 1 1 1 3 7 14 29 59 118 237 475 14 397 10 = 110001101 2 0 1 3 6 12 24 49 99 198 397 1 1 0 0 0 1 1 0 1 15 x 4 (n = 4) / 1 2 1 1001 1110 1111 2 1010 1101 1110 3 1011 1100 1101 4 1100 1011 1100 5 1101 1010 1011 6 1110 1001 1010 7 1111 1000 1001 8 1000 1 11
16 (1) 10 10 2 01010 2, 10110 (2) 7 10 2, 00111 17 2 00010 2 10 2, 2 10 Nagisa ISHIURA 1 12