random numbers generation using unfair coin in any range

import random

# Step 1: Biased coin
def rand01():
    return 1 if random.uniform(0, 1) > 0.8 else 0

# Step 2: Convert to fair coin
def fair_rand01():
    while True:
        a = rand01()
        b = rand01()
        if a == 0 and b == 1:
            return 0
        elif a == 1 and b == 0:
            return 1

# Step 3: Directly generate 1 to 10
def rand1to10():
    while True: #here range is 1 to 10 means 10 number so look for smallest value of 2 which make it either 10 or more ie 2^4
        num = (
            fair_rand01() * 8 +
            fair_rand01() * 4 +
            fair_rand01() * 2 +
            fair_rand01()
        )

        if num < 10:   # accept only 0–9
            return num + 1
#Another example when the numbers to generate are 4 to 10 where the range is 7 number and 2^3=8 which is just above 7
def rand4to10():
    while True:
        num = fair_rand01()*4 + fair_rand01()*2 + fair_rand01()  # 0–7
        if num < 7:
            return num + 4

# Test
for _ in range(20):
    print(rand1to10())