Use 4 bits to represent the decimal number -610 in sign and size code \( 00110_{2} \) \( 1110_{2} \) \( 11110_{2} \) \( 0110_{2} \)

To represent the decimal number -610 using 4 bits in sign and magnitude (S&M) code, we need to follow these steps: 1. Convert the absolute value of the decimal number to binary. 2. Add a sign bit to the left of the binary number, where 0 represents positive and 1 represents negative. Let's start with the absolute value of -610, which is 610. 1. Convert 610 to binary: 610 / 2 = 305 remainder 0 305 / 2 = 152 remainder 1 152 / 2 = 76 remainder 0 76 / 2 = 38 remainder 0 38 / 2 = 19 remainder 0 19 / 2 = 9 remainder 1 9 / 2 = 4 remainder 1 4 / 2 = 2 remainder 0 2 / 2 = 1 remainder 0 1 / 2 = 0 remainder 1 Reading the remainders from bottom to top, we get the binary representation of 610 as 1001101102. 2. Since we are using 4 bits, we need to truncate the binary number to fit within the 4-bit limit. The binary number 1001101102 is 10 bits long, so we take the rightmost 4 bits to get 01102. 3. Add the sign bit: Since the original number is negative, we add a 1 as the sign bit. The final 4-bit sign and magnitude code for -610 is 1110. Therefore, the correct answer is: \( 1110_{2} \)