Question

2) Answer the following number base questions. (SHOW ALL WORK)
a. What is 1AA2h in decimal?
do not simplfy
b. What is 238in hex? (put your answer in into word format)
c. What is -126 in binary ?
d. What is -128 in binary?

e. Using the binary compliment method , subtract 11001b – 10110b

Answer 1

a) Answer

Hexadecimal numbers are a base 16(from 0 to 9 and A=10,B=11,C=12,D=13,E=14,F=15) numbers and decimal numbers are a base 10 numbers(from 0 to 9). Any hexadecimal number having digit/letter post F is considered as an incorrect hexadecimal number. SO the number 1AA2h consist of h so it's an invalid number, but if it is without h we can calculate it. To find hexadecimal to decimal we need to multiply every digit with 16 to the power of digit location.

1AA2=1*16^3+10^2+10^1+2^0=6818

b) Answer

Since 238 is a decimal number, So let's convert it to a hexadecimal number

238/16= 14.875, So take the remainder out and multiply with 16, the result 14 will be considered as E in Hexadecimal

0.875*16=14 which is E in Hexadecimal

So the answer is EE

c) Answer

We use the leftmost digit of the number as a special value to represent the sign of the number: 0 = positive, 1 = negative

-126 in binary= 1 1111110

d) Answer

-128 in binary= 1 10000000

e) Answer

11001– 10110= Find two's complement of 10110 which is 1010, now subtract it which is 1111