Question

Assume 151 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate 151 - 214 using saturating arithmetic. The result should be written in decimal. Show your work.

Short answer

The result of performing saturating arithmetic of 152-214 is as follows:$-105+42=-63$

Step-by-step solution

Determine the addition and subtraction showing carries

The binary values of the signed decimal numbers will be used for addition and subtraction. For addition the right most bits will be added and the carry will be forwarded through left. The operands should have the values that fits 32 bits or specified bits . The subtraction will takes place from the right most bits and the borrowed bits will be considered as carry.

Determine 151-214 using saturating arithmetic.

Given that , the 151 and 214 are signed 8 bit decimal integers that are stored in a 2’s complement format.

Convert each of decimal numbers to binary:

151 = 10010111₂

214 = 11010110₂

Now take 2’s Complement for both the numbers:

Convert all the 1s to 0s and 0s to 1s . Then add 1 to the converted number.

151 = 10010111₂

2's Complement = 01101000

Add 1 = 01101000 + 1

2's Complement = 01101001

214 = 11010110₂

2's complement = 00101001

Add 1 = 00101001 + 1

2's complement = 00101010

Now, convert them in to decimal numbers:

151= -105

214=42

For , subtraction use the converted decimal numbers:

-105+42 = -63

Therefore, the result of 151-214=-63