Question

Add the following unsigned hexadecimal numbers and indicate whether or not the addition causes an overflow of an 8-bit result. Show your work, to include your conversion from hexadecimal to binary. a. 15 16 +2 A 16b. A3 16+C 16 Find the difference of the following decimal numbers to 6-bit two's complement binary numbers and subtract them. Indicate if the difference overflows a 6-bit result. Show your work, to include your conversion from decimal to binary two's complement. a. 56 10 −51 10 b. −16 10 −21 10

Answer 1

Adding hexadecimal numbers and finding the difference in two's complement binary needs conversion of the numbers into the relevant formats first. None of the addition or subtraction operations of the examples given lead to an overflow in their respective bit sizes. It's essential to follow the correct rules of addition and subtraction for positive and negative numbers.

Step-by-step explanation:

Adding unsigned hexadecimal numbers and determining overflow for an 8-bit result can be done by first converting the hex values to binary and then performing the addition.

• a. 1516 + 2A16: Convert to binary: 1516 = 000101012, 2A16 = 001010102. Add: 001111112 (no overflow occurs).
• b. A316 + C16: Convert to binary: A316 = 101000112, C16 = 000011002. Add: 101011112 (no overflow occurs).

• a. 5610 - 5110: Convert to 6-bit two's complement binary: 5610 = 1110002, 5110 = 1100112. Subtract: 0011012 (no overflow occurs).
• b. -1610 - 2110:: Convert to 6-bit two's complement binary: -1610 = 1010002, -2110 = 1000112. Subtract: 0001012 (no overflow occurs).

When performing arithmetic operations with numbers, it's important to follow the rules for addition and subtraction. For example, when two positive numbers are added, the result will have a positive sign, while two negative numbers will produce a negative result. When subtracting, change the sign of the number being subtracted and proceed with addition according to these rules. Overflow occurs when the result of the addition or subtraction does not fit within the number of bits allocated for the result.