diff --git a/packages/opentelemetry-core/src/context/propagation/B3Propagator.ts b/packages/opentelemetry-core/src/context/propagation/B3Propagator.ts
index d801082acaa..aba6290d66a 100644
--- a/packages/opentelemetry-core/src/context/propagation/B3Propagator.ts
+++ b/packages/opentelemetry-core/src/context/propagation/B3Propagator.ts
@@ -37,6 +37,7 @@ export const DEBUG_FLAG_KEY = Context.createKey(
 const VALID_TRACEID_REGEX = /^([0-9a-f]{16}){1,2}$/i;
 const VALID_SPANID_REGEX = /^[0-9a-f]{16}$/i;
 const INVALID_ID_REGEX = /^0+$/i;
+const VALID_SAMPLED_VALUES = [true, 'true', '1'];
 
 function isValidTraceId(traceId: string): boolean {
   return VALID_TRACEID_REGEX.test(traceId) && !INVALID_ID_REGEX.test(traceId);
@@ -64,7 +65,7 @@ export class B3Propagator implements HttpTextPropagator {
       isValidSpanId(spanContext.spanId)
     ) {
       if (parentSpanId) {
-        if (isValidTraceId(parentSpanId as string)) {
+        if (isValidSpanId(parentSpanId as string)) {
           setter(carrier, X_B3_PARENT_SPAN_ID, parentSpanId);
         } else {
           return;
@@ -104,7 +105,9 @@ export class B3Propagator implements HttpTextPropagator {
     const options = parseHeader(sampledHeader);
     const debugHeaderValue = parseHeader(flagsHeader);
     const debug = debugHeaderValue === '1';
-    const traceFlagsOrDebug = Number(debug) || Number(options);
+    const isSampled = VALID_SAMPLED_VALUES.includes(options);
+    const traceFlags =
+      debug || isSampled ? TraceFlags.SAMPLED : TraceFlags.NONE;
 
     if (
       typeof traceIdHeaderValue !== 'string' ||
@@ -124,8 +127,7 @@ export class B3Propagator implements HttpTextPropagator {
         traceId,
         spanId,
         isRemote: true,
-        // Set traceFlags as 1 if debug is 1
-        traceFlags: traceFlagsOrDebug || TraceFlags.NONE,
+        traceFlags,
       });
     }
     return context;
diff --git a/packages/opentelemetry-core/test/context/B3Propagator.test.ts b/packages/opentelemetry-core/test/context/B3Propagator.test.ts
index 7d9c59be66f..733c448df00 100644
--- a/packages/opentelemetry-core/test/context/B3Propagator.test.ts
+++ b/packages/opentelemetry-core/test/context/B3Propagator.test.ts
@@ -287,6 +287,71 @@ describe('B3Propagator', () => {
       assert.equal(context.getValue(DEBUG_FLAG_KEY), undefined);
       assert.equal(context.getValue(PARENT_SPAN_ID_KEY), undefined);
     });
+    it('should extract context of a span from carrier when debug flag is invalidly set as false', () => {
+      carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
+      carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
+      carrier[X_B3_FLAGS] = 'false';
+      carrier[X_B3_SAMPLED] = '0';
+      const context = b3Propagator.extract(
+        Context.ROOT_CONTEXT,
+        carrier,
+        defaultGetter
+      );
+      const extractedSpanContext = getExtractedSpanContext(context);
+
+      assert.deepStrictEqual(extractedSpanContext, {
+        spanId: 'b7ad6b7169203331',
+        traceId: '0af7651916cd43dd8448eb211c80319c',
+        isRemote: true,
+        traceFlags: TraceFlags.NONE,
+      });
+      assert.equal(context.getValue(DEBUG_FLAG_KEY), undefined);
+      assert.equal(context.getValue(PARENT_SPAN_ID_KEY), undefined);
+    });
+
+    it('should extract context of a span from carrier when debug flag is invalidly set as true', () => {
+      carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
+      carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
+      carrier[X_B3_FLAGS] = 'true';
+      carrier[X_B3_SAMPLED] = '0';
+      const context = b3Propagator.extract(
+        Context.ROOT_CONTEXT,
+        carrier,
+        defaultGetter
+      );
+      const extractedSpanContext = getExtractedSpanContext(context);
+
+      assert.deepStrictEqual(extractedSpanContext, {
+        spanId: 'b7ad6b7169203331',
+        traceId: '0af7651916cd43dd8448eb211c80319c',
+        isRemote: true,
+        traceFlags: TraceFlags.NONE,
+      });
+      assert.equal(context.getValue(DEBUG_FLAG_KEY), undefined);
+      assert.equal(context.getValue(PARENT_SPAN_ID_KEY), undefined);
+    });
+
+    it('should extract context of a span from carrier when debug flag is invalidly set as 2', () => {
+      carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
+      carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
+      carrier[X_B3_FLAGS] = '3';
+      carrier[X_B3_SAMPLED] = '0';
+      const context = b3Propagator.extract(
+        Context.ROOT_CONTEXT,
+        carrier,
+        defaultGetter
+      );
+      const extractedSpanContext = getExtractedSpanContext(context);
+
+      assert.deepStrictEqual(extractedSpanContext, {
+        spanId: 'b7ad6b7169203331',
+        traceId: '0af7651916cd43dd8448eb211c80319c',
+        isRemote: true,
+        traceFlags: TraceFlags.NONE,
+      });
+      assert.equal(context.getValue(DEBUG_FLAG_KEY), undefined);
+      assert.equal(context.getValue(PARENT_SPAN_ID_KEY), undefined);
+    });
 
     it('should extract context of a span from carrier with a parent span id', () => {
       carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
@@ -311,6 +376,29 @@ describe('B3Propagator', () => {
       assert.equal(context.getValue(PARENT_SPAN_ID_KEY), 'f4592dc481026a8c');
     });
 
+    it('should extract context of a span from carrier with a parent span id and debug set', () => {
+      carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
+      carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
+      carrier[X_B3_PARENT_SPAN_ID] = 'f4592dc481026a8c';
+      carrier[X_B3_FLAGS] = '1';
+      carrier[X_B3_SAMPLED] = '0';
+      const context = b3Propagator.extract(
+        Context.ROOT_CONTEXT,
+        carrier,
+        defaultGetter
+      );
+      const extractedSpanContext = getExtractedSpanContext(context);
+
+      assert.deepStrictEqual(extractedSpanContext, {
+        spanId: 'b7ad6b7169203331',
+        traceId: '0af7651916cd43dd8448eb211c80319c',
+        isRemote: true,
+        traceFlags: TraceFlags.SAMPLED,
+      });
+      assert.equal(context.getValue(DEBUG_FLAG_KEY), '1');
+      assert.equal(context.getValue(PARENT_SPAN_ID_KEY), 'f4592dc481026a8c');
+    });
+
     it('should return undefined when traceId is undefined', () => {
       carrier[X_B3_TRACE_ID] = undefined;
       carrier[X_B3_SPAN_ID] = undefined;
@@ -339,6 +427,16 @@ describe('B3Propagator', () => {
       assert.deepStrictEqual(context, undefined);
     });
 
+    it('should return undefined when parentSpanId is a trace id', () => {
+      carrier[X_B3_TRACE_ID] = '0af7651916cd43dd8448eb211c80319c';
+      carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
+      carrier[X_B3_PARENT_SPAN_ID] = '0af7651916cd43dd8448eb211c80319d';
+      const context = getExtractedSpanContext(
+        b3Propagator.extract(Context.ROOT_CONTEXT, carrier, defaultGetter)
+      );
+      assert.deepStrictEqual(context, undefined);
+    });
+
     it('returns undefined if b3 header is missing', () => {
       const context = getExtractedSpanContext(
         b3Propagator.extract(Context.ROOT_CONTEXT, carrier, defaultGetter)
@@ -357,7 +455,7 @@ describe('B3Propagator', () => {
     it('extracts b3 from list of header', () => {
       carrier[X_B3_TRACE_ID] = ['0af7651916cd43dd8448eb211c80319c'];
       carrier[X_B3_SPAN_ID] = 'b7ad6b7169203331';
-      carrier[X_B3_SAMPLED] = '01';
+      carrier[X_B3_SAMPLED] = '1';
       const context = b3Propagator.extract(
         Context.ROOT_CONTEXT,
         carrier,