diff --git a/flang/lib/Optimizer/CodeGen/CodeGen.cpp b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
--- a/flang/lib/Optimizer/CodeGen/CodeGen.cpp
+++ b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
@@ -727,8 +727,10 @@
   mlir::LogicalResult
   matchAndRewrite(fir::ConvertOp convert, OpAdaptor adaptor,
                   mlir::ConversionPatternRewriter &rewriter) const override {
-    auto fromTy = convertType(convert.getValue().getType());
-    auto toTy = convertType(convert.getRes().getType());
+    auto fromFirTy = convert.getValue().getType();
+    auto toFirTy = convert.getRes().getType();
+    auto fromTy = convertType(fromFirTy);
+    auto toTy = convertType(toFirTy);
     mlir::Value op0 = adaptor.getOperands()[0];
     if (fromTy == toTy) {
       rewriter.replaceOp(convert, op0);
@@ -750,8 +752,7 @@
       return rewriter.create<mlir::LLVM::FPExtOp>(loc, toTy, val);
     };
     // Complex to complex conversion.
-    if (fir::isa_complex(convert.getValue().getType()) &&
-        fir::isa_complex(convert.getRes().getType())) {
+    if (fir::isa_complex(fromFirTy) && fir::isa_complex(toFirTy)) {
       // Special case: handle the conversion of a complex such that both the
       // real and imaginary parts are converted together.
       auto zero = mlir::ArrayAttr::get(convert.getContext(),
@@ -773,6 +774,22 @@
                                                              ic, one);
       return mlir::success();
     }
+
+    // Follow UNIX F77 convention for logicals:
+    // 1. underlying integer is not zero => logical is .TRUE.
+    // 2. logical is .TRUE. => set underlying integer to 1.
+    auto i1Type = mlir::IntegerType::get(convert.getContext(), 1);
+    if (fromFirTy.isa<fir::LogicalType>() && toFirTy == i1Type) {
+      mlir::Value zero = genConstantIndex(loc, fromTy, rewriter, 0);
+      rewriter.replaceOpWithNewOp<mlir::LLVM::ICmpOp>(
+          convert, mlir::LLVM::ICmpPredicate::ne, op0, zero);
+      return mlir::success();
+    }
+    if (fromFirTy == i1Type && toFirTy.isa<fir::LogicalType>()) {
+      rewriter.replaceOpWithNewOp<mlir::LLVM::ZExtOp>(convert, toTy, op0);
+      return mlir::success();
+    }
+
     // Floating point to floating point conversion.
     if (isFloatingPointTy(fromTy)) {
       if (isFloatingPointTy(toTy)) {
diff --git a/flang/test/Fir/convert-to-llvm.fir b/flang/test/Fir/convert-to-llvm.fir
--- a/flang/test/Fir/convert-to-llvm.fir
+++ b/flang/test/Fir/convert-to-llvm.fir
@@ -1288,7 +1288,8 @@
 // CHECK-LABEL: llvm.func @select_case_logical(
 // CHECK-SAME:                                 %[[ARG0:.*]]: !llvm.ptr<i32>
 // CHECK:         %[[LOAD_ARG0:.*]] = llvm.load %[[ARG0]] : !llvm.ptr<i32>
-// CHECK:         %[[SELECT_VALUE:.*]] = llvm.trunc %[[LOAD_ARG0]] : i32 to i1
+// CHECK:         %[[CST_ZERO:.*]] = llvm.mlir.constant(0 : i64) : i32
+// CHECK:         %[[SELECT_VALUE:.*]] = llvm.icmp "ne" %[[LOAD_ARG0]], %[[CST_ZERO]] : i32
 // CHECK:         %[[CST_FALSE:.*]] = llvm.mlir.constant(false) : i1
 // CHECK:         %[[CST_TRUE:.*]] = llvm.mlir.constant(true) : i1
 // CHECK:         %[[CMPEQ:.*]] = llvm.icmp "eq" %[[SELECT_VALUE]], %[[CST_FALSE]] : i1