Question

For the first three sections assume unsigned integers.

1. Convert to binary and hexadecimal
   1. 85
   2. 4563
2. Convert from binary to decimal and hexadecimal.
   1. 0b1010 1011
   2. 0b0011 0001
3. Convert from hexadecimal to binary and decimal.
   1. 0xB2
   2. 0x11

Answer 1

Convert to binary

1. 85-1010101

Steps

Number 85

divide by 2
result	42	remainder	1(LSB)
divide by 2
result	21	remainder	0
divide by 2
result	10	remainder	1
divide by 2
result	5	remainder	0
divide by 2
result	2	remainder	1
divide by 2
result	1	remainder	0
divide by 2
result	0	remainder	1(MSB)

b. 4563-1000111010011

Steps

Number 4563

divide by 2
result	2281	remainder	1(LSB)
divide by 2
result	1140	remainder	1
divide by 2
result	570	remainder	0
divide by 2
result	285	remainder	0
divide by 2
result	142	remainder	1
divide by 2
result	71	remainder	0
divide by 2
result	35	remainder	1
divide by 2
result	17	remainder	1
divide by 2
result	8	remainder	1
divide by 2
result	4	remainder	0
divide by 2
result	2	remainder	0
divide by 2
result	1	remainder	0
divide by 2
result	0	remainder	1 (MSB)

Convert to hexadecimal

a. 85₁₀=55₁₆

Convert 85₁₀ to hex:

Division by 16	Quotient	Remainder (decimal)	Remainder (hex)	Digit #
85/16	5	5	5	0
5/16	0	5	5	1

b. 4563₁₀=11D3₁₆

Convert 4563₁₀ to hex:

Division by 16	Quotient	Remainder (decimal)	Remainder (hex)	Digit #
4563/16	285	3	3	0
285/16	17	13	D	1
17/16	1	1	1	2
1/16	0	1	1	3

Convert from binary to decimal

a. 1010 1011=171

1010 1011=(1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 171

b.0011 0001=49

00110001 = (0 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = 49

Convert from binary to hexadecimal

a. 1010 1011=AB

b.0011 0001=31