Final answer:
To convert decimal numbers to different bases using subtraction or division-remainder, divide the number repeatedly by the base and record the remainders. Use the remainders, read from bottom to top, to determine the equivalent value in the desired base.
Step-by-step explanation:
To perform the given base conversions using subtraction or division-remainder, we divide the decimal number repeatedly by the base (10) and record the remainders. The remainders, read from bottom to top, give us the equivalent value in the desired base.
a) 45810 = ?
To convert 45810 to base 2 (binary), we divide repeatedly by 2, recording the remainders: 458 ÷ 2 = 229 remainder 0, 229 ÷ 2 = 114 remainder 1, 114 ÷ 2 = 57 remainder 0, 57 ÷ 2 = 28 remainder 1, 28 ÷ 2 = 14 remainder 0, 14 ÷ 2 = 7 remainder 0, 7 ÷ 2 = 3 remainder 1, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. The binary equivalent of 45810 is 111001010.
b) 67710 = ?
To convert 67710 to base 8 (octal), we divide repeatedly by 8, recording the remainders: 677 ÷ 8 = 84 remainder 5, 84 ÷ 8 = 10 remainder 4, 10 ÷ 8 = 1 remainder 2, 1 ÷ 8 = 0 remainder 1. The octal equivalent of 67710 is 1245.
c) 151810 = ?
To convert 151810 to base 16 (hexadecimal), we divide repeatedly by 16, recording the remainders: 1518 ÷ 16 = 94 remainder 14 (E in hexadecimal), 94 ÷ 16 = 5 remainder 14 (E in hexadecimal), 5 ÷ 16 = 0 remainder 5. The hexadecimal equivalent of 151810 is 5EE.
d) 440110 = ?
To convert 440110 to base 12, we divide repeatedly by 12, recording the remainders: 4401 ÷ 12 = 366 remainder 9, 366 ÷ 12 = 30 remainder 6, 30 ÷ 12 = 2 remainder 6, 2 ÷ 12 = 0 remainder 2. The base 12 equivalent of 440110 is 2669.