Practice Solution 2 -- Two's Complement

Practice Homework Solution 2 --

Convert the following numbers from the bases as indicated.

a.      1A7   (hex)                ___000110100111_______  (binary)

b.      372   (octal)              ____011111010_________ (binary)

c.      110111010101 (binary)      ____6725______________ (octal)

d.      10010101011  (binary)      ____4AB_______________ (hex)

e.      372   (octal)              ____FA________________ (hex)

f.      1A7   (hex)                ____647_______________ (octal)

What is the biggest numeric value you can write in 8 bits using two's complement notation? Express it in both binary two's complement form and in decimal:
```
two's comp  ___01111111_______________  decimal  ___127__________________
```
What is the smallest numeric value you can write in 8 bits using two's complement notation? Express it in both binary two's complement form and in decimal:
```
two's comp  ___10000000_______________  decimal  ___-128_________________
```

Convert the following decimal values to binary two's complement notation in 8 bits:

a.	84		___01010100___________

b.	-84		___10101100___________

c.	15		___00001111___________

d.	-15		___11110001___________

e.	0		___00000000___________

f.	-128		___10000000___________

Is it possible to express +128 in 8 bits using two's complement notation? If so, then write it below.
```
_______no_______________
```
Is it possible to express +128 in 8 bits if we use unsigned numbers? If so, then write it below.
```
___10000000_____________
```
What is the biggest value we can express in 8 bits if we use unsigned numbers? Express it in both binary and in decimal:
```
binary  ____11111111______________  decimal  ___255__________________
```
What is the smallest value we can express in 8 bits if we use unsigned numbers? Express it in both binary and in decimal:
```
binary  ____00000000______________  decimal  ___0____________________
```

What are the decimal values of the following numbers, given that they are written using two's complement notation?

a.	01100111		________103___________

b.	10011110		________-98___________

c.	10000000		________-128__________

d.	11111111		________-1____________

e.	11111110		________-2____________

How can you distinguish a positive number from a negative number without doing any calculations if you see them expressed in 8-bit two's complement notation?
```
Look at the sign bit.
```

Suppose we use a machine that represents integers in 4 bits using two's complement notation.

a.	Our integers act like what set of modulo numbers?  ___mod 16________

b.	How many integers can be represented in the machine? ___16__________

c.	What is the largest possible positive integer?  Express it in both binary and decimal.

	binary:  ___0111________________  decimal:  ___7__________________

d.	What is the smallest possible negative integer?  Express it in both binary and decimal.

	binary:  ___1000________________  decimal:  ___-8_________________

What is the smallest number of bits that can be used to store an integer on a computer which must be able to handle integers ranging from 1,000,000 down to -1,000,000?
```
____21_________________
```