Convert decimal integers to binary, octal, and hexadecimal.

Here are the solutions to your questions. QUESTION ONE a) Convert 57_10 into binary To convert a decimal integer to binary, we repeatedly divide the decimal number by 2 and record the remainders. We then read the remainders from bottom to top. Step 1: Divide 57 by 2. 57 ÷ 2 = 28 R 1 Step 2: Divide 28 by 2. 28 ÷ 2 = 14 R 0 Step 3: Divide 14 by 2. 14 ÷ 2 = 7 R 0 Step 4: Divide 7 by 2. 7 ÷ 2 = 3 R 1 Step 5: Divide 3 by 2. 3 ÷ 2 = 1 R 1 Step 6: Divide 1 by 2. 1 ÷ 2 = 0 R 1 Reading the remainders from bottom to top gives the binary equivalent. 57_10 = 111001_2 b) Convert 4937_10 into octal To convert a decimal integer to octal, we repeatedly divide the decimal number by 8 and record the remainders. We then read the remainders from bottom to top. Step 1: Divide 4937 by 8. 4937 ÷ 8 = 617 R 1 Step 2: Divide 617 by 8. 617 ÷ 8 = 77 R 1 Step 3: Divide 77 by 8. 77 ÷ 8 = 9 R 5 Step 4: Divide 9 by 8. 9 ÷ 8 = 1 R 1 Step 5: Divide 1 by 8. 1 ÷ 8 = 0 R 1 Reading the remainders from bottom to top gives the octal equivalent. 4937_10 = 11511_8 c) Convert 53241_10 into hexadecimal To convert a decimal integer to hexadecimal, we repeatedly divide the decimal number by 16 and record the remainders. Remainders 10-15 are represented by letters A-F. We then read the remainders from bottom to top. Step 1: Divide 53241 by 16. 53241 ÷ 16 = 3327 R 9 Step 2: Divide 3327 by 16. 3327 ÷ 16 = 207 R 15 (which is F in hexadecimal) Step 3: Divide 207 by 16. 207 ÷ 16 = 12 R 15 (which is F in hexadecimal) Step 4: Divide 12 by 16. 12 ÷ 16 = 0 R 12 (which is C in hexadecimal) Reading the remainders from bottom to top gives the hexadecimal equivalent. 53241_10 = CFF9_16 d) Convert 511.80625_10 into binary This conversion involves two parts: the integer part and the fractional part. Integer Part (511_10 to binary): Repeatedly divide the integer part by 2 and record the remainders. 511 ÷ 2 = 255 R 1 255 ÷ 2 = 127 R 1 127 ÷ 2 = 63 R $