README.MD

Section 00

Number Representation

./section-00.pdf

1 Unsigned Integers

1.1.1 Convert the following numbers from their initial radix into the other two common radices

(a) 0b10010011 -decimal-> 147
	       -hex-> 0x93

(b) 0xD3AD     -decimal-> 54189
	       -binary-> 1101 0011 1010 1101

(c) 63	       -binary-> 0011 1111
	       -hex-> 0x3F

(d) 0b00100100 -decimal-> 36
	       -hex-> 0x24

(e) 0xB33F     -decimal-> 45887
	       -binary-> 1011 0011 0011 1111

(g) 39	       -binary-> 0010 0111
	       -hex-> 0x27

(h) 0x7EC4     -decimal-> 32452
	       -binary-> 0111 1110 1100 0100

(i) 437        -binary-> 0001 1011 0101
	       -hex-> 0x1B5

2 Signed Integers

2.1 Two's compliment

MSB has a negative value, all others are positive.

Assume 8-bit integers, answer for cases unsigned integers, biased bias -127, two's compliment.

2.2.1 What is the largest integer? The largest integer’s representation + 1?

• (a) [Unsigned] 255, 0
• (b) [Biased] 128, -127
• (c) [Two’s Complement] 127, -128

2.2.2 How do you represent the numbers 0, 1, and -1?

• (a) [Unsigned] 0000 0000, 0000 0001, -
• (b) [Biased] 0111 1111, 1000 0000, 0111 1110
• (c) [Two’s Complement] 0000 0000, 0000 0001, 1111 1111

2.2.3 How do you represent 17, -17?

• (a) [Unsigned] 0001 0001, -
• (b) [Biased] 1001 0000, 0110 1110
• (c) [Two’s Complement] 0001 0001, 1110 1111

2.2.6 Explain where each of the three radices shines and why it is preferred over other bases in a given context.

• binary - computers
• decimal - humans
• hex - shorthand for binary, inbetween

3 Counting

Bitstrings can be used to represent anything inside the computer n bits can be used to represent 2^n distinct things

3.1.1 How many bits do we need to represent a variable that can only take on the values 0, π or e?

2

3.1.3 If the only value a variable can take on is e, how many bits are needed to represent it?

0