In most cases, you want to parse more than one hex byte at once. In those cases, use the hex crate.

parse this into an integer

You want to use from_str_radix. It's implemented on the integer types.

use std::i64;

fn main() {
    let z = i64::from_str_radix("1f", 16);
    println!("{:?}", z);
}

If your strings actually have the 0x prefix, then you will need to skip over them. The best way to do that is via trim_start_matches or strip_prefix:

use std::i64;

fn main() {
    let raw = "0x1f";
    let without_prefix = raw.trim_start_matches("0x");
    let z = i64::from_str_radix(without_prefix, 16);
    println!("{:?}", z);
}

Without the 0x prefix, you need to specify the base explicitly, otherwise there's no way to tell:

x = int("deadbeef", 16)

With the 0x prefix, Python can distinguish hex and decimal automatically:

>>> print(int("0xdeadbeef", 0))
3735928559
>>> print(int("10", 0))
10

(You must specify 0 as the base in order to invoke this prefix-guessing behavior; if you omit the second parameter, int() will assume base-10.)

• Rustfmt is a tool for automatically formatting Rust code to the community-accepted style.
• Clippy is a tool for finding common mistakes that may not be compilation errors but are unlikely to be what the programmer intended.

Rustfmt points out that you are using 3-space indents (Rust uses 4), and that some of your lines don't need to be split.

Clippy points out:

warning: returning the result of a let binding from a block
 --> src/main.rs:9:5
  |
7 |     let to_binary = hex[2..].chars().map(|c| to_binary(c)).collect();
  |     ----------------------------------------------------------------- unnecessary let binding
8 |
9 |     to_binary
  |     ^^^^^^^^^
  |
  = note: #[warn(clippy::let_and_return)] on by default
  = help: for further information visit https://rust-lang.github.io/rust-clippy/master/index.html#let_and_return
help: return the expression directly
  |
7 |
8 |
9 |     hex[2..].chars().map(|c| to_binary(c)).collect()
  |

warning: redundant closure found
 --> src/main.rs:7:42
  |
7 |     let to_binary = hex[2..].chars().map(|c| to_binary(c)).collect();
  |                                          ^^^^^^^^^^^^^^^^ help: remove closure as shown: `to_binary`
  |
  = note: #[warn(clippy::redundant_closure)] on by default
  = help: for further information visit https://rust-lang.github.io/rust-clippy/master/index.html#redundant_closure

There's no reason to return a String here, a &'static str is lighter-weight. See What are the differences between Rust's String and str? for full details, but a String requires a heap allocation, while a &'static str is a reference to some existing data in the compiled binary.

With these changes, all of your tests pass:

fn main() {
    let binary_value = convert_to_binary_from_hex("0x39A7F8");
    println!("Converted: {}", binary_value);
}

fn convert_to_binary_from_hex(hex: &str) -> String {
    hex[2..].chars().map(to_binary).collect()
}

fn to_binary(c: char) -> &'static str {
    match c {
        '0' => "0000",
        '1' => "0001",
        '2' => "0010",
        '3' => "0011",
        '4' => "0100",
        '5' => "0101",
        '6' => "0110",
        '7' => "0111",
        '8' => "1000",
        '9' => "1001",
        'A' => "1010",
        'B' => "1011",
        'C' => "1100",
        'D' => "1101",
        'E' => "1110",
        'F' => "1111",
        _ => "",
    }
}

In fact, deleting all of your code causes your tests to pass. It would be a good idea to add some tests!

Depending on what routes you want to look down next, you could try:

• to handle strings that do not start with 0x without panicking.
• to handle upper- and lower-case hex
• to reduce/avoid string munging yourself

The zeo disappears, because you reserve space for 16 hex chars only, but u require 64 hex chars. Please also verify if sha256 has can really be stored in an u64 integer!

You’re overthinking the whole thing.

assert_eq!(format!("{:x}", 42), "2a");
assert_eq!(format!("{:X}", 42), "2A");

That’s from std::fmt::LowerHex and std::fmt::UpperHex, respectively. See also a search of the documentation for "hex".

A couple of things:

1. Any time you have a function which could fail, it should return an Option<T>. Ask yourself, if someone calls convert_to_hex_from_binary("foobar") and gets back "", is that reasonable? They will need to manually check that their input makes sense, or that the output makes sense every time. Static checking of these errors is part of the joy of Rust.

With that it mind, change to_hex like so:

fn to_hex(b: &str) -> Option<&str> {
    match b {
        "0000" => Some("0"),
        "0001" => Some("1"),
        "0010" => Some("2"),
        "0011" => Some("3"),
        "0100" => Some("4"),
        "0101" => Some("5"),
        "0110" => Some("6"),
        "0111" => Some("7"),
        "1000" => Some("8"),
        "1001" => Some("9"),
        "1010" => Some("A"),
        "1011" => Some("B"),
        "1100" => Some("C"),
        "1101" => Some("D"),
        "1110" => Some("E"),
        "1111" => Some("F"),
        _ => None,
    }
}

2. You are iterating over a known range of values to get counter. Instead of using a while loop, you can use a range. Since you're now returning None from to_hex you can now shortcut returning if something is wrong with None.

Your inner loop now looks like this:

let mut hex_string = String::new();
for counter in (0..padded_binary.len()).step_by(4) {
    match to_hex(&padded_binary[counter..counter + 4])
    {
        Some(converted) => hex_string.push_str(converted),
        None => return None
    };
}

Your function signature and return type also need to match Option<String>:

fn convert_to_hex_from_binary(binary: &str) -> Option<String> {
    ...
    Some(hex_string)
}

3. Your padded_binary definition can be simplified, since repeating "0" zero times is exactly the same as not repeating it.

The definition is simply:

let padded_binary = ["0".repeat(padding_count), binary.to_string()].concat();

A couple of non Rust specific things:

1. Consider writing some tests.

2. String representation of binary numbers often begin with '0b'. For example 0b1101 == 13. You might want to consider checking for this prefix on the input string and trimming it.

3. You may have already thought about this, but consider if you want to trim whitespace or leave it to the function caller.