Converting Decimal to Binary and 2's Complement Representation

1. How do you convert the decimal number 149 to simple binary? 2. How do you convert the numbers +121 and -121 to 2's complement 8-bit binary numbers?

To convert the decimal number 149 to simple binary, we divide the number repeatedly by 2 until the quotient becomes 0. The remainders obtained in each division, read in reverse order, give us the binary representation. Here's the calculation: 149 ÷ 2 = 74 (remainder 1) 74 ÷ 2 = 37 (remainder 0) 37 ÷ 2 = 18 (remainder 1) 18 ÷ 2 = 9 (remainder 0) 9 ÷ 2 = 4 (remainder 1) 4 ÷ 2 = 2 (remainder 0) 2 ÷ 2 = 1 (remainder 0) 1 ÷ 2 = 0 (remainder 1) Reading the remainders in reverse order, the binary representation of 149 is 10010101. To convert the numbers +121 and -121 to 2's complement 8-bit binary numbers: a) +121 in simple binary: 121 ÷ 2 = 60 (remainder 1) 60 ÷ 2 = 30 (remainder 0) 30 ÷ 2 = 15 (remainder 0) 15 ÷ 2 = 7 (remainder 1) 7 ÷ 2 = 3 (remainder 1) 3 ÷ 2 = 1 (remainder 1) 1 ÷ 2 = 0 (remainder 1) Reading the remainders in reverse order, the simple binary representation of +121 is 01111001. b) -121 in 2's complement 8-bit binary: First, we represent the absolute value of -121 in simple binary: 121 ÷ 2 = 60 (remainder 1) 60 ÷ 2 = 30 (remainder 0) 30 ÷ 2 = 15 (remainder 0) 15 ÷ 2 = 7 (remainder 1) 7 ÷ 2 = 3 (remainder 1) 3 ÷ 2 = 1 (remainder 1) 1 ÷ 2 = 0 (remainder 1) The simple binary representation of 121 is 01111001. To obtain the 2's complement representation of -121, we invert the bits (changing 0s to 1s and 1s to 0s) and add 1 to the least significant bit. Inverting the bits: 10000110 Adding 1: 10000111

Converting Decimal Number to Binary

Converting decimal number 149 to binary involves dividing the number by 2 repeatedly and noting down the remainders in reverse order. This process helps in converting a decimal number into its binary form. In this case, we converted 149 to binary as 10010101 by following the steps mentioned earlier.

Converting to 2's Complement Representation

When dealing with signed integers in binary, representing negative numbers in 2's complement form is essential. To convert +121 to simple binary, we divide the positive number by 2 and then read the remainders in reverse order to get the binary representation. On the other hand, converting -121 to 2's complement binary involves finding the simple binary of the absolute value, inverting the bits, and adding 1 to achieve the final 2's complement representation.
← Tips for using a straight razor blade for precise cuts Troubleshooting common issues in refrigeration systems →