diff --git a/compiler/src/parsing/lexer.mll b/compiler/src/parsing/lexer.mll
index 55546f7c09..2d701c9ae5 100644
--- a/compiler/src/parsing/lexer.mll
+++ b/compiler/src/parsing/lexer.mll
@@ -191,6 +191,7 @@ rule token = parse
   | "}" { RBRACE }
   | "[" { LBRACK }
   | "]" { RBRACK }
+  | "^" { CARET }
   | "<" { LCARET }
   | ">" { RCARET }
   | "^" { CARET }
@@ -202,7 +203,9 @@ rule token = parse
   | "%" { PERCENT }
   | "<=" { LESSEQ }
   | ">=" { GREATEREQ }
+  | "&" { AMP }
   | "&&" { AMPAMP }
+  | "|" { PIPE }
   | "||" { PIPEPIPE }
   | "!" { NOT }
   | '"'   { read_dquote_str (Buffer.create 16) lexbuf }
diff --git a/compiler/src/parsing/parser.dyp b/compiler/src/parsing/parser.dyp
index 11ac630851..91d66cfbc3 100644
--- a/compiler/src/parsing/parser.dyp
+++ b/compiler/src/parsing/parser.dyp
@@ -22,7 +22,7 @@ include Parser_header
 %token LBRACK RBRACK LPAREN LPARENNOSPACE RPAREN LBRACE RBRACE LCARET RCARET
 %token CARET
 %token COMMA SEMI AS
-%token THICKARROW ARROW PIPE
+%token THICKARROW ARROW
 %token IS ISNT EQEQ LESSEQ GREATEREQ
 %token EQUAL GETS
 %token UNDERSCORE
@@ -35,6 +35,7 @@ include Parser_header
 
 %token LET MUT REC IF WHEN ELSE MATCH WHILE
 %token AMPAMP PIPEPIPE NOT
+%token AMP PIPE
 
 %token ENUM RECORD IMPORT EXPORT FOREIGN WASM PRIMITIVE
 %token EXCEPT FROM
@@ -127,11 +128,17 @@ binop_expr :
   | binop_expr(<=p80) isnt_op eols?      binop_expr(<p80) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p80
   | binop_expr(<=p80) eqeq_op eols?      binop_expr(<p80) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p80
   | binop_expr(<=p80) noteq_op eols?     binop_expr(<p80) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p80
+  | binop_expr(<=p60) caret_op eols?     binop_expr(<p60) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p60
   | binop_expr(<=p90) lcaret_op eols?    binop_expr(<p90) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p90
+  | binop_expr(<=p100) llcaret_op eols?   binop_expr(<p100) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p100
   | binop_expr(<=p90) rcaret_op eols?    binop_expr(<p90) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p90
+  | binop_expr(<=p100) rrcaret_op eols?   binop_expr(<p100) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p100
+  | binop_expr(<=p90) rrrcaret_op eols?  binop_expr(<p100) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p100
   | binop_expr(<=p90) lesseq_op eols?    binop_expr(<p90) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p90
   | binop_expr(<=p90) greatereq_op eols? binop_expr(<p90) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p90
+  | binop_expr(<=p70) amp_op eols?       binop_expr(<p70) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p70
   | binop_expr(<=p40) ampamp_op eols?    binop_expr(<p40) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p40
+  | binop_expr(<=p50) pipe_op eols?      binop_expr(<p50) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p50
   | binop_expr(<=p30) pipepipe_op eols?  binop_expr(<p30) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p30
   | binop_expr(<=p110) plusplus_op eols?  binop_expr(<p110) { Exp.apply ~loc:(symbol_rloc dyp) (mkid_expr dyp [$2]) [$1; $4] } p110
   | binop_expr colon typ { Exp.constraint_ ~loc:(symbol_rloc dyp) $1 $3 } p140
@@ -278,16 +285,28 @@ eqeq_op :
   | EQEQ { "==" }
 noteq_op :
   | NOT EQUAL { "!=" }
+caret_op :
+  | CARET { "^" }
 lcaret_op :
   | LCARET { "<" }
+llcaret_op :
+  | LCARET LCARET { "<<" }
 rcaret_op :
   | RCARET { ">" }
+rrcaret_op :
+  | RCARET RCARET { ">>" }
+rrrcaret_op :
+  | RCARET RCARET RCARET { ">>>" }
 lesseq_op :
   | LESSEQ { "<=" }
 greatereq_op :
   | GREATEREQ { ">=" }
+amp_op :
+  | AMP { "&" }
 ampamp_op :
   | AMPAMP { "&&" }
+pipe_op :
+  | PIPE { "|" }
 pipepipe_op :
   | PIPEPIPE { "||" }
 pluseq_op :
@@ -312,11 +331,17 @@ infix_op :
   | eqeq_op
   | plusplus_op
   | noteq_op
+  | caret_op
   | lcaret_op
+  | llcaret_op
   | rcaret_op
+  | rrcaret_op
+  | rrrcaret_op
   | lesseq_op
   | greatereq_op
+  | amp_op
   | ampamp_op
+  | pipe_op
   | pipepipe_op
   | pluseq_op
   | dasheq_op
diff --git a/compiler/test/test_end_to_end.re b/compiler/test/test_end_to_end.re
index 51d1a3b537..b92c44c140 100644
--- a/compiler/test/test_end_to_end.re
+++ b/compiler/test/test_end_to_end.re
@@ -190,6 +190,24 @@ let basic_functionality_tests = [
   t("or2", "true || false", "true"),
   t("or3", "false || true", "true"),
   t("or4", "false || false", "false"),
+  t("land1", "1 & 1", "1"),
+  t("land2", "1 & 0", "0"),
+  t("land3", "0 & 1", "0"),
+  t("land4", "0 & 0", "0"),
+  t("lor1", "1 | 1", "1"),
+  t("lor2", "1 | 0", "1"),
+  t("lor3", "0 | 1", "1"),
+  t("lor4", "0 | 0", "0"),
+  t("lxor1", "1 ^ 1", "0"),
+  t("lxor2", "1 ^ 0", "1"),
+  t("lxor3", "0 ^ 1", "1"),
+  t("lxor4", "0 ^ 0", "0"),
+  t("lsl1", "7 << 1", "14"),
+  t("lsl2", "0 << 1", "0"),
+  t("lsr1", "7 >>> 1", "3"),
+  t("lsr2", "0 >>> 1", "0"),
+  t("asr1", "179 >> 1", "89"),
+  t("asr2", "0 >> 1", "0"),
   t("comp1", "if (2 < 3) {true} else {false}", "true"),
   te("comp1e", "if (2 < 3) {true} else {3}", "type"),
   t("comp2", "if (2 <= 3) {true} else {false}", "true"),
diff --git a/docs/contributor/operator_precedence.md b/docs/contributor/operator_precedence.md
index 8484053b09..69f5e83016 100644
--- a/docs/contributor/operator_precedence.md
+++ b/docs/contributor/operator_precedence.md
@@ -12,12 +12,12 @@ This table shows which operators take precedence over other operators, and can b
 | 130 | Exponentiation | right-to-left | NYI |
 | 120 | Multiplication<br>Division<br>Modulus | left-to-right | `… * …`<br>`… / …`<br>`… % …` |
 | 110 | Addition<br>Subtraction<br>String Concatenation | left-to-right | `… + …`<br>`… - …`<br>`… ++ …` |
-| 100 | Bitwise Shift Left<br>Bitwise Shift Right<br>Bitwise Arithmetic Shift Right | left-to-right | NYI |
+| 100 | Bitwise Shift Left<br>Bitwise Shift Right<br>Bitwise Arithmetic Shift Right | left-to-right | `… << …` <br> `… >> …` <br> `… >>> …` |
 | 90 | Less Than<br>Less Than or Equal To<br>Greater Than<br>Greater Than or Equal To | left-to-right | `… < …`<br>`… <= …`<br>`… > …`<br>`… >= …` |
 | 80 | Structural Equality<br>Structural Inequality<br>Physical Equality<br>Physical Inequality | left-to-right | `… == …`<br>`… != …`<br>`… is …`<br>`… isnt …`(NYI) |
-| 70 | Bitwise AND | left-to-right | NYI |
-| 60 | Bitwise XOR | left-to-right | NYI |
-| 50 | Bitwise OR | left-to-right | NYI |
+| 70 | Bitwise AND | left-to-right | `… & …` |
+| 60 | Bitwise XOR | left-to-right | `… ^ …` |
+| 50 | Bitwise OR | left-to-right | `… | …` |
 | 40 | Logical AND | left-to-right | `… && …` |
 | 30 | Logical OR | left-to-right | `… \|\| …` |
 | 20 | Ternary Conditional | right-to-left | NYI |
diff --git a/stdlib/pervasives.gr b/stdlib/pervasives.gr
index c265cfb0d9..baeac8dd6d 100644
--- a/stdlib/pervasives.gr
+++ b/stdlib/pervasives.gr
@@ -18,13 +18,13 @@ import foreign wasm numberGreaterEqual : (Number, Number) -> Bool as (>=) from '
 // Number bit/logical operations
 import foreign wasm numberLnot : Number -> Number as lnot from 'stdlib-external/runtime'
 
-import foreign wasm numberLand : (Number, Number) -> Number as land from 'stdlib-external/runtime'
-import foreign wasm numberLor : (Number, Number) -> Number as lor from 'stdlib-external/runtime'
-import foreign wasm numberLxor : (Number, Number) -> Number as lxor from 'stdlib-external/runtime'
+import foreign wasm numberLand : (Number, Number) -> Number as (&) from 'stdlib-external/runtime'
+import foreign wasm numberLor : (Number, Number) -> Number as (|) from 'stdlib-external/runtime'
+import foreign wasm numberLxor : (Number, Number) -> Number as (^) from 'stdlib-external/runtime'
 
-import foreign wasm numberLsl : (Number, Number) -> Number as lsl from 'stdlib-external/runtime'
-import foreign wasm numberLsr : (Number, Number) -> Number as lsr from 'stdlib-external/runtime'
-import foreign wasm numberAsr : (Number, Number) -> Number as asr from 'stdlib-external/runtime'
+import foreign wasm numberLsl : (Number, Number) -> Number as (<<) from 'stdlib-external/runtime'
+import foreign wasm numberLsr : (Number, Number) -> Number as (>>>) from 'stdlib-external/runtime'
+import foreign wasm numberAsr : (Number, Number) -> Number as (>>) from 'stdlib-external/runtime'
 
 
 // Number coercions & conversions